Conservative leader David Cameron is the new UK prime minister after the resignation of Gordon Brown.
Mr Cameron, 43, entered 10 Downing Street after travelling to Buckingham Palace to formally accept the Queen's request to form the next government.
He said he aimed to form a "proper and full coalition" with the Lib Dems to provide "strong, stable government".
His party won the most seats in the UK general election last week, but not an overall majority.
In a speech outside his new Downing Street home, Mr Cameron said he and Lib Dem leader Nick Clegg would "put aside party differences and work hard for the common good and the national interest".
He paid tribute to outgoing PM Gordon Brown for his long years of public service and said he would tackle Britain's "pressing problems" - the deficit, social problems and to "rebuild trust in our political system".
Mr Cameron stressed there would be "difficult decisions" but said he wanted to take people through them to reach "better times ahead".
He said he aimed to "help build a more responsible society here in Britain... Those who can should and those who can't, we will always help. I want to make sure that my government always looks after the elderly, the frail, the poorest in our country.
"We must take everyone through with us on some of the difficult decisions we have ahead."
"I came into politics because I love this country, I think it's best days still lie ahead and I believe deeply in public service.
"I think the service our country needs right now is to face up to our big challenges, to confront our problems, take difficult decisions, lead people through those decisions, so that together we can reach better times ahead."
Lib Dem agreement
The Conservatives have been in days of negotiations with the Lib Dems - who were also negotiating with Labour - after the UK election resulted in a hung parliament.
Lib Dem leader Nick Clegg must get the support of a majority of his MPs and his party's ruling body, the federal executive, before he can enter into a coalition.
Earlier the Lib Dems said talks with Labour failed because "the Labour Party never took seriously the prospects of forming a progressive, reforming government".
A spokesman said key members of the Labour team "gave every impression of wanting the process to fail" and the party had made "no attempt at all" to agree a common approach on issues like schools funding and tax reform.
"Certain key Labour cabinet ministers were determined to undermine any agreement by holding out on policy issues and suggesting that Labour would not deliver on proportional representation and might not marshal the votes to secure even the most modest form of electoral reform," he said.
However Labour's Lord Mandelson told the BBC they had been "up for" a deal with the Lib Dems, but they had "created so many barriers and obstacles that perhaps they thought their interests lay on the Tory side, on the Conservative side, rather than the progressive side".
'My fault'
After it became clear the talks had failed, Mr Brown tendered his resignation and said he wished the next prime minister well.
In an emotional resignation statement outside Number Ten, Mr Brown thanked his staff, his wife Sarah and their children, who joined the couple as they left for Buckingham Palace.
Mr Brown said it had been "a privilege to serve" adding: "I loved the job not for its prestige, its titles and its ceremony - which I do not love at all. No, I loved the job for its potential to make this country I love fairer, more tolerant, more green, more democratic, more prosperous and more just - truly a greater Britain."
He also paid tribute to the courage of the armed forces, adding: "I will never forget all those who have died in honour and whose families today live in grief."
Later he thanked Labour activists and MPs for all their efforts and told them Labour's general election performance was "my fault, and my fault alone".
The Lib Dem and Conservative teams met for hours of negotiations at the Cabinet Office on Tuesday - four days after the UK general election resulted in a hung parliament.
The talks resumed after Lib Dem negotiators met a Labour team, which followed Mr Brown's announcement on Monday that he would step down as Labour leader by September.
But there were signs throughout the afternoon that the two parties - who together would still not command an overall majority in the House of Commons - would not reach a deal.
Edit: This post is for informing you and discusion. Personally I was surprised it all was agreed with the lib-dems today.
Plans for five-year, fixed-term parliaments, meaning the next election would not take place until May 2015. The coalition would last for a full parliament.
The Lib Dems have agreed to drop plans for a "mansion tax" on properties costing more than £2m, while the Conservatives have ditched their pledge to raise the inheritance tax threshold to £1m
The BBC's Robert Peston says the Lib Dem policy of taxing planes, rather than passengers, has been adopted and there will be a commitment to a new tax or levy on banks. He also says there will be a "significant move" towards raising the income tax threshold to £10,000 in the first budget,
The new administration will scrap part of Labour's planned rise in National Insurance
A pledge to have a referendum on any further transfer of powers to the EU and a commitment from the Lib Dems not to adopt the euro for the lifetime of the next Parliament
The Lib Dems have agreed to Tory proposals for a cap on non-EU migration
The Conservatives will recognise marriage in the tax system, but Lib Dems will abstain in Commons vote
The Lib Dems will drop opposition to a replacement for Britain's Trident nuclear missiles but the programme will be scrutinised for value for money
There will be a referendum on moving to the Alternative Vote system and enhanced "pupil premium" for deprived children as Lib Dems demanded
I SUPPORT THE CONSERVATIVES! - but i found this funny!
Mr Cameron, 43, entered 10 Downing Street after travelling to Buckingham Palace to formally accept the Queen's request to form the next government.
He said he aimed to form a "proper and full coalition" with the Lib Dems to provide "strong, stable government".
His party won the most seats in the UK general election last week, but not an overall majority.
In a speech outside his new Downing Street home, Mr Cameron said he and Lib Dem leader Nick Clegg would "put aside party differences and work hard for the common good and the national interest".
He paid tribute to outgoing PM Gordon Brown for his long years of public service and said he would tackle Britain's "pressing problems" - the deficit, social problems and to "rebuild trust in our political system".
Mr Cameron stressed there would be "difficult decisions" but said he wanted to take people through them to reach "better times ahead".
He said he aimed to "help build a more responsible society here in Britain... Those who can should and those who can't, we will always help. I want to make sure that my government always looks after the elderly, the frail, the poorest in our country.
"We must take everyone through with us on some of the difficult decisions we have ahead."
"I came into politics because I love this country, I think it's best days still lie ahead and I believe deeply in public service.
"I think the service our country needs right now is to face up to our big challenges, to confront our problems, take difficult decisions, lead people through those decisions, so that together we can reach better times ahead."
Lib Dem agreement
The Conservatives have been in days of negotiations with the Lib Dems - who were also negotiating with Labour - after the UK election resulted in a hung parliament.
Lib Dem leader Nick Clegg must get the support of a majority of his MPs and his party's ruling body, the federal executive, before he can enter into a coalition.
Earlier the Lib Dems said talks with Labour failed because "the Labour Party never took seriously the prospects of forming a progressive, reforming government".
A spokesman said key members of the Labour team "gave every impression of wanting the process to fail" and the party had made "no attempt at all" to agree a common approach on issues like schools funding and tax reform.
"Certain key Labour cabinet ministers were determined to undermine any agreement by holding out on policy issues and suggesting that Labour would not deliver on proportional representation and might not marshal the votes to secure even the most modest form of electoral reform," he said.
However Labour's Lord Mandelson told the BBC they had been "up for" a deal with the Lib Dems, but they had "created so many barriers and obstacles that perhaps they thought their interests lay on the Tory side, on the Conservative side, rather than the progressive side".
'My fault'
After it became clear the talks had failed, Mr Brown tendered his resignation and said he wished the next prime minister well.
In an emotional resignation statement outside Number Ten, Mr Brown thanked his staff, his wife Sarah and their children, who joined the couple as they left for Buckingham Palace.
Mr Brown said it had been "a privilege to serve" adding: "I loved the job not for its prestige, its titles and its ceremony - which I do not love at all. No, I loved the job for its potential to make this country I love fairer, more tolerant, more green, more democratic, more prosperous and more just - truly a greater Britain."
He also paid tribute to the courage of the armed forces, adding: "I will never forget all those who have died in honour and whose families today live in grief."
Later he thanked Labour activists and MPs for all their efforts and told them Labour's general election performance was "my fault, and my fault alone".
The Lib Dem and Conservative teams met for hours of negotiations at the Cabinet Office on Tuesday - four days after the UK general election resulted in a hung parliament.
The talks resumed after Lib Dem negotiators met a Labour team, which followed Mr Brown's announcement on Monday that he would step down as Labour leader by September.
But there were signs throughout the afternoon that the two parties - who together would still not command an overall majority in the House of Commons - would not reach a deal.
Edit: This post is for informing you and discusion. Personally I was surprised it all was agreed with the lib-dems today.
There will be a "significant acceleration" of efforts to reduce the budget deficit - including £6bn of spending reductions this year. An emergency Budget will take place within 50 daysEDit: New details DETAILS OF THE AGREEMENT!
2323: Details of the Tory-Lib Dem deal emerge. The Lib Dems have agreed to drop plans for a "mansion tax", while the Conservatives have ditched their pledge to raise the inheritance tax threshold to £1m. The new administration will scrap Labour's planned rise in National Insurance but some of the benefits will go to reducing income tax thresholds for lower earners.
2317: Conservative Andrew Lansley will become health secretary, the BBC learns. There is still no confirmation of who will be home secretary.
Lib-dems will receive 20 seats in government! 5 in the cabinet! 1 of which is nick clegg as deputy prime minister!
2332: The Lib Dems have agreed to a cap on immigration and a commitment not to join the euro for the lifetime of the parliament.
2336Lib Dem Danny Alexander is to become Scottish secretary, the BBC learns. The Lib Dems are expected to get about 20 government jobs in total.
2340: The first full meeting of the coalition cabinet is expected to take place on Wednesday.
2303: Lib Dem leader Nick Clegg is the new deputy prime minister, Downing Street confirms.
2256: Liam Fox is confirmed as defence secretary.
GEORGE Osborne confirmed as chancellor of exchequer ! NOOOOOOOO I am a conservative supporter and even I wanted vince!
2356: More on the details of the coalition deal. The Lib Dems agreed to an emergency budget within 50 days and to Tory a budget reduction plan including £6bn in cuts to non-frontline services in 2010/11. The two sides also agreed a commitment to a replacement for the Trident nuclear missile system but the programme will be scrutinised for value for money
0001: Prime Minister David Cameron and his deputy Nick Clegg are due to outline the full details of the coalition government later, as it begins its first complete day in office.
PM: David Cameron
Deputy PM: Nick Clegg
Foreign Sec: William Hague
Chancellor: George Osborne
Business/banking: Vince Cable
Defence: Liam Fox
Health: Andrew Lansley
Energy/Climate: Chris Huhne
Justice Sec: Ken Clarke
Home Sec: Theresa May
Business: Vince Cable
Schools: Michael Gove
Chief Sec to Treasury: David Laws
Scottish Secretary: Danny Alexander
Plans for five-year, fixed-term parliaments, meaning the next election would not take place until May 2015. The coalition would last for a full parliament.
The Lib Dems have agreed to drop plans for a "mansion tax" on properties costing more than £2m, while the Conservatives have ditched their pledge to raise the inheritance tax threshold to £1m
The BBC's Robert Peston says the Lib Dem policy of taxing planes, rather than passengers, has been adopted and there will be a commitment to a new tax or levy on banks. He also says there will be a "significant move" towards raising the income tax threshold to £10,000 in the first budget,
The new administration will scrap part of Labour's planned rise in National Insurance
A pledge to have a referendum on any further transfer of powers to the EU and a commitment from the Lib Dems not to adopt the euro for the lifetime of the next Parliament
The Lib Dems have agreed to Tory proposals for a cap on non-EU migration
The Conservatives will recognise marriage in the tax system, but Lib Dems will abstain in Commons vote
The Lib Dems will drop opposition to a replacement for Britain's Trident nuclear missiles but the programme will be scrutinised for value for money
There will be a referendum on moving to the Alternative Vote system and enhanced "pupil premium" for deprived children as Lib Dems demanded
I SUPPORT THE CONSERVATIVES! - but i found this funny!