Cameron takes the helm as new PM
The Tory leader said he intended to form a "proper and full" coalition government with the Liberal Democrats.
Arriving in Downing Street with his wife Samantha, he announced: "Her Majesty the Queen has asked me to form a new Government and I have accepted."
Mr Cameron paid tribute to Gordon Brown for his "long record of dedicated public service" and said that after more than a decade of Labour rule, Britain was "more open at home and more compassionate abroad".
Looking ahead to the coalition he will form with the Lib Dems, he said: "We have some deep and pressing problems - a huge deficit, deep social problems, a political system in need of reform.
"For those reasons, I aim to form a proper and full coalition between the Conservatives and the Liberal Democrats. I believe that is the right way to provide this country with the strong, the stable, the good and decent government that I think we need so badly."
Mr Cameron went on: "Nick Clegg and I are both political leaders who want to put aside party differences and work hard for the common good and for the national interest. I believe that is the best way to get the strong Government that we need, decisive Government that we need today.
"I came into politics because I love this country, I think its best days still lie ahead and I believe deeply in public service, and I think the service our country needs right now is to face up to our really big challenges, to confront our problems, to take difficult decisions, to lead people through those difficult decisions so that together we can reach better times ahead."
The Prime Minister went on: "One of the tasks that we clearly have is to rebuild trust in our political system. Yes, that's about cleaning up expenses, yes, that's about reforming parliament, and yes, it's about making sure people are in control and that the politicians are always their servants and never their masters.
"But I believe it's also something else - it's about being honest about what government can achieve. Real change is not what government can do on its own, real change is when everyone pulls together, comes together, works together, when we all exercise our responsibilities to ourselves, our families, to our communities and to others."
http://uk.news.yahoo.com/5/20100511/video/vuk-brown-resigns-thank-you-and-goodbye-37e89e1.html
Gordon Brown is no longer Britain's prime minister after handing his resignation to the Queen and walking out of Downing Street with his wife and two children.
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Speaking outside No 10, he said: "I wish the next prime minister well as he makes the important choices for the future."
Mr Brown added: "Above all it was a privilege to serve. And yes, I loved the job."
He finished his speech saying: "As I leave the second most important job I could ever hold, I cherish even more the first - as a husband and a father. Thank you and goodbye."
Before visiting the Queen at Buckingham Palace, Mr Brown revealed he was to advise she should appoint Conservative leader David Cameron as the UK's new leader.
Later, while thanking his supporters and former colleagues at Labour's headquarters, Mr Brown announced Harriet Harman will be the party's acting leader.
He said: "There is a strong, progressive majority in Britain. I wish, more than I could possibly say, that I could have mobilised that majority to carry the election.
"But I could not and I have to accept, and indeed assert, personal responsibility. The fault is mine and I will carry that alone."
Former home secretary David Blunkett said: "This is a sad moment... there can be few tasks in life as thankless as being prime minister.
"This is true in spades when dealing with a global recession in which everywhere else in the world is affected - but your own electorate have no-one else to blame but you."
Mr Brown had previously declared he was prepared to step down after last week's General Election resulted in a hung parliament.
But the latest revelations followed Sky sources revealing how talks between Labour and the Liberal Democrats to form a coalition government "never got off the ground".
After Mr Brown quit, a Lib Dem spokesperson said in a statement that "key Labour cabinet ministers were determined to undermine any agreement".
The statement added: "It is clear that some people in the Labour Party see opposition as a more attractive alternative to the challenges of creating a progressive, reforming government."
Senior Lib Dem MP Vince Cable had earlier told Sky a deal on forming a coalition between his party and the Conservatives is "very, very close to being done".
The Tories have agreed a three-year deal with the Lib Dems, which would allow them three budgets to get the
economy back on track, Sky sources said.
Talking about the negotiations, Sky's chief political correspondent Jon Craig said senior Tory sources were claiming the Lib Dems have "dropped their controversial policy of an amnesty for illegal immigrants".
Craig said: "There are concessions on the Tories' side too, particularly on tax.
"It seems tax breaks for married couples will go, according to Conservative MPs I have spoken to, and that, I'm told, will anger many of the right-wing of the
Conservative Party."
Mr Brown now wants to step away from politics and move on to charity work and literature, Sky sources added.