David Cameron will begin today to forge the first peacetime coalition for more than 80 years after becoming Britain's 53rd Prime Minister.
The new government will include five Liberal Democrats in Cabinet and some 15 others in ministerial jobs.
Nick Clegg was last night confirmed by the queen as Deputy Prime Minister.
He and Mr Clegg would "put political differences aside" as they moved to tackle the deficit, ease deep social problems, rebuild public trust in politics and bring about a more responsible society. The maxim of his government would be: "Those who can, should, those who cannot, we will always help".
He promised that the elderly, frail and poorest would not be forgotten.
The scale of the political revolution under way -- and the extent of the two leaders' collaboration -- was underlined with the unprecedented announcement that the next election will take place on the first Thursday in May 2015.
Even before taking office, Mr Cameron gave up the Prime Minister's freedom to go the country when he chooses, with both sides instead committing to a full five-year term.
Last night Clegg won the backing of his party for the deal.
The hiatus since polling closed last Thursday had seemed interminable, and at times fatal, to Tory hopes, but shortly before 9pm the waiting ended as Mr Cameron swept into Downing Street in a silver Jaguar amid cheers and jeers from a crowd of many hundreds gathered in Whitehall.
He went round the car to open the door for his wife, Samantha. Together they walked to the same spot outside No 10 where, 90 minutes earlier, Gordon Brown had bid an emotional farewell to his home of the past 1,048 days.
He wished his successor well, said that it had been a privilege to serve, paid a glowing tribute to the Armed Forces and, his voice cracking, to wife Sarah.
He not only stepped down as Prime Minister but also as leader of the Labour Party and has signalled his intention to quit as an MP.
Mr Cameron, with his pregnant wife looking on nervously, walked through the front door and straight into the realities of his new job: his first security briefing and telephone calls from President Obama and Chancellor Merkel of Germany. His first appointments were George Osborne as Chancellor and William Hague as Foreign Secretary.
Mr Cameron is the youngest Prime Minister since Lord Liverpool in 1812. He is a few months younger than Mr Blair was when he took up office, also aged 43.
Many in politics believed that David Cameron was bound to be Prime Minister one day. School friends recall the alarmingly self-confident young man sitting at the breakfast table, proudly announcing that one day he would lead the Conservative Party.
At Eton, he was quite unintimidated by arriving at this vast and forbidding school. But he was nearly expelled for smoking and it was that shock which prompted him to concentrate on his studies.
When he took politics at A-level, it was the making of him.
But was he really planning to be Prime Minister even then? Former headmaster Eric Anderson defends young Cameron, saying that when he -- Anderson -- was 14 he wanted to play rugby for Scotland, but that didn't mean there was the faintest prospect of it happening.
John Clarke, who taught Cameron politics as he prepared for entrance to Oxford, says: "He was very much a late developer academically, one who came good once he did a series of subjects that suited him.
"He didn't make a great splash at Eton, but, of all the people I taught, he was one of the most impressive."