Arriving from his audience at Buckingham Palace where he formally "kissed hands" with the Queen, the Conservative leader said he intended to form a "full and proper" coalition with the Liberal Democrats.
With his wife Samantha by his side, he declared: "This is going to be tough and difficult work.
"Coalition will throw up all sorts of difficulties but I believe that together we can provide that strong and stable government that our country needs."
His arrival was marked by a telephone call from President Barack Obama in the White House congratulating him on his appointment.
Less than two hours earlier, Gordon Brown had emerged to announce that he was making his own journey to the Palace to tender his resignation, bringing down the curtain on 13 years of Labour government.
His emotional statement - on the steps of No 10 - brought to an end five days of uncertainty after the General Election resulted in the first hung parliament in a generation.
Sources confirmed tonight that Mr Cameron's close ally George Osborne will be the new Chancellor of the Exchequer while William Hague is Foreign Secretary.
It was reported that Andrew Lansley would go to the Department of Health, keeping his shadow cabinet portfolio.
But much of the shape of the new Government was unclear.
Even as Mr Cameron was entering No 10, the deal thrashed out by Conservative and Lib Dem negotiating teams had still to be approved by Lib Dem MPs, who were meeting in Westminster tonight.
It is expected the Lib Dems will be given a number of Cabinet posts, with speculation that Nick Clegg will be made deputy prime minister.
Mr Cameron said he and the Lib Dem leader were both prepared to put aside their 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, the decisive Government that we need today," he said.
"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 these difficult decisions so that together we can reach better times ahead."
Downing Street said that during their telephone call, President Obama had invited Mr Cameron to visit the US in July and said he was looking forward to seeing him in June at the G8 and G20 meetings.
Mr Cameron also received a congratulatory call from German Chancellor Angela Merkel who invited him to visit Berlin "at the earliest possible opportunity".
Mr Cameron was greeted with loud cheers as he walked slowly up the last steps to the door of No 10 hand-in-hand with his wife.
There was more rapturous applause as he arrived tonight for a meeting of Conservative MPs and peers in the House of Commons.
The day began with Labour still hoping that it could strike a deal with the Lib Dems that would enable it to remain in office.
Following a meeting of the two parties' negotiating teams, Energy Secretary Ed Miliband described the talks as "constructive" with "many points of agreement" between them.
But by late afternoon it was becoming apparent that the talks were going nowhere. Health Secretary Andy Burnham became the first minister to state publicly that Labour needed to respect the result of election which they "didn't win".
His comments echoed similar calls from former Cabinet ministers David Blunkett and John Reid that Labour should accept it had been defeated and allow the Conservatives to form a government.
Shortly after 7.15pm Mr Brown bowed to the inevitable, appearing in Downing Street for the final time to announce that he was going to the Palace to tender his resignation and to advise the Queen to appoint Mr Cameron as his successor.
With his wife Sarah and two young sons John and Fraser watching, he said it had been a "privilege to serve" during his three short years as premier.
"Yes, 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 said.
"In the face of many challenges in a few short years, challenges up to and including the global financial meltdown, I have always strived to serve, to do my best in the interest of Britain, its values and its people."
He also confirmed that he was standing down as Labour leader with immediate effect. His deputy, Harriet Harman, will take over until a permanent successor is chosen.
Following his audience at the Palace, he then returned to Labour Party headquarters in Victoria to pay an emotional farewell to party workers and Cabinet ministers who had gathered there.
Behind the first recriminations were beginning, with the Lib Dems issuing an angry statement blaming Labour for the breakdown of their talks, saying the party "never took seriously" the prospect of forming a coalition.
"Key members of Labour's negotiating team gave every impression of wanting the process to fail," a Lib Dem spokesman said.
"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, not least in the context of a Labour leadership election campaign."
Meanwhile Alastair Campbell, Tony Blair's former communications chief who has been advising Mr Brown, said he believed the Lib Dems had made a mistake in striking an agreement with the Tories.
"I think the Liberal Democrats will regret what they are doing. A lot of Liberal Democrat voters have voted Liberal Democrat to stop there being a Tory government and I think they will feel very badly let down," he said.
VIEW GALLERY
Comments