London, England (CNN) -- Within hours of his appointment, Britain's new prime minister, David Cameron, immediately began forming his coalition government overnight, appointing several Liberal Democrat leaders to Cabinet posts along with members of his own Conservative Party.
Lib Dems leader Nick Clegg, who was named deputy prime minister, announced early Wednesday his party's agreement into entering such a partnership, saying, "I hope this is the start of the new politics I have always believed in: diverse, plural; where politicians of different persuasions come together to overcome their differences in order to deliver good government for the sake of the whole country."
Clegg sought to allay party members' concerns going into the arrangement.
"I am acutely aware that I carry your hopes and aspirations with me into this coalition agreement," he said. "I can imagine this evening you will have many questions and maybe many doubts about this new governing arrangement.
"But I want to assure you that I wouldn't have entered into this agreement unless I was genuinely convinced that it offers a unique opportunity to deliver the kind of changes that you and I believe in."
In addition to Clegg's appointment, a source from the Conservative Party said Conservative Parliament member George Osborne has been named chancellor of the exchequer and former Conservative Party leader William Hague has been appointed secretary for foreign affairs. Four other Cabinet posts will be filled by Liberal Democrats, Downing Street said.
Queen Elizabeth II named Cameron prime minister Tuesday night, shortly after Gordon Brown resigned, Buckingham Palace said.
Brown had said Monday he would step down as leader of his party by the fall, but he changed course Tuesday, announcing he was quitting his party post immediately. His party came in second, behind the Conservatives, in parliamentary elections last week, but no party won an absolute majority.
Cameron becomes the country's first Conservative prime minister since the Labour Party, under Tony Blair, defeated John Major in 1997.
Cameron echoed U.S. President John F. Kennedy's famous "ask not what your country can do for you" speech in his first remarks as prime minister.
He aims to build a society "where we don't just ask, 'What are my entitlements?' but 'What are my responsibilities?'... Where we don't ask, 'What am I owed?' but more 'What can I give?'" Cameron said.
"Those who can, should, and those who can't, we will always help," he promised, stressing freedom, fairness and responsibility.
"Real change is not about what government can do," he insisted. "Real change is when everyone pulls together, comes together, works together."
He also praised his Brown in brief remarks outside the prime minister's residence before disappearing into 10 Downing Street with his wife, Samantha.
Coalition governments are extremely rare in British politics.
The last time there was a "hung parliament" with no party holding a majority of the seats in the House of Commons was 1974. Coalition talks then between the Conservatives and Liberals failed, and a short-lived minority Labour government took power.
But Cameron said Tuesday he aims "to form a proper and full coalition between the Conservatives and the Liberal Democrats," saying it would be "the right way to provide this country with the strong, the stable, the good and decent government that I believe we need so badly."
The two parties would command a clear majority in the 650-seat House of Commons, but have a number of key policy differences.
Cameron said he wants "to put aside party differences and work together for the common good and the national interest."
Earlier Tuesday, U.S. President Barack Obama called Cameron shortly after the new prime minister entered Downing Street, according to a statement from the White House.
During the call, Obama said he extended his congratulations and invited Cameron and his wife to visit the White House this summer.
"This historic election has been closely followed by the American people, and I have no doubt that the ties between our two countries will continue to thrive in the years to come," Obama's statement said.
Cameron's appointment ended nearly a week of uncertainty, since the Conservatives won 306 seats in the 650-seat House of Commons -- 20 short of a majority. Brown's Labour Party got 258, and Clegg's Liberal Democrats got 57.
Smaller parties got 28 seats, and one will be decided in an election later this month after one of the candidates died during the campaign.
The results set off a round of haggling, first between the Conservatives and Liberal Democrats, and then between the Lib Dems and Labour.
Brown dramatically announced Monday night that he would step aside as leader of the Labour Party by autumn. It was apparently an effort to clear the way for a deal between his party and the Liberal Democrats.
Though they have more in common ideologically with Labour than the Conservatives, the Liberal Democrats, after talks Tuesday morning with Labour, said they were going back to the Conservatives.
Brown then sped up his timetable, announcing he was quitting his party post immediately and resigning as prime minister.
His deputy, Harriet Harman, will lead the Labour Party until a leadership contest can be held, he told party activists.
In his brief resignation statement, Brown said he loved the job of prime minister not for pomp and ceremony but "for its potential to make this country I love fairer, more tolerant, more green, more democratic, more prosperous and more just."
Cameron is Queen Elizabeth II's 13th prime minister -- including Harold Wilson twice, for his two non-consecutive terms -- since she was crowned in 1952.