David Cameron is spending the weekend finalising his first all-Conservative cabinet after his party won a majority in Thursday's election.
Speaking outside 10 Downing Street after visiting Buckingham Palace, he said the UK was "on the brink of something special".
The Conservatives have 331 seats - five more than needed for a Commons majority - their first such victory since 1992.
Mr Cameron's rivals Ed Miliband, Nick Clegg and Nigel Farage have all resigned after election disappointment.
The PM has already reappointed Chancellor George Osborne, who has also been made first secretary of state.
Theresa May, Philip Hammond and Michael Fallon retain their jobs at the Home Office, Foreign Office and Defence with other announcements due on Monday.
Meanwhile Labour and the Lib Dems are beginning the search for new leaders.
- Chuka Umunna, Andy Burnham and Yvette Cooper have all been tipped as potential Labour leadership contenders after Ed Miliband stepped down.
- Tim Farron and Norman Lamb are among the frontrunners to succeed Nick Clegg after he said he would quit as Lib Dem leader.
- SNP leader Nicola Sturgeon will meet all her party's 56 new MPs in Edinburgh after it swept the board in Scotland
- Nigel Farage has recommended Suzanne Evans take over as interim UKIP leader after he said he would step down. Douglas Carswell, the party's one MP, ruled himself out of the running
- The new Westminster Parliament will see a record number of female and ethnic representatives, with 191 women (up from 143) and 42 from an ethnic minority (up from 27).
Mr Cameron said he would reach out to all parts of the UK and strive to "bring the country together" in the wake of the Scottish National Party (SNP)'s election landslide in Scotland - where it won 56 of the 59 seats.
The SNP is expected to press for more devolved powers for the Scottish Parliament, going beyond what was proposed by the Smith Commission after last year's independence referendum.
The Conservatives' victory means they will be able to govern without the need for a coalition or a formal agreement with other parties.
Mr Cameron said he had spoken to both Mr Miliband and Mr Clegg, paying tribute to the latter's contribution to the coalition government over the past five years.
Speaking in Downing Street, he said: "We will govern as a party of one nation, one United Kingdom.
"That means ensuring this recovery reaches all parts of our country, from north to south, to east to west."
"I have always believed in governing with respect," he said "That's why in the last parliament we devolved power to Scotland and Wales, and gave the people of Scotland a referendum on whether to stay inside the United Kingdom.
"In this parliament I will stay true to my word and implement as fast as I can the devolution that all parties agreed for Wales, Scotland and Northern Ireland."
The Conservatives have said they will seek to deliver all of their election manifesto in government, focusing on tax cuts, extending access to childcare, extending home ownership and giving the public a say on the UK's future membership of the EU.
Leading Eurosceptic backbencher Mark Pritchard told the BBC there would be no pressure for the prime minister to rush into discussions about an in-out referendum on the UK's future in Europe, which he has pledged to hold in 2017.
Mr Pritchard said the prime minister would need time to try to negotiate new terms for the UK's membership.
"The party will be 100% behind the PM as he goes off to Brussels to fight for Britain, and indeed fight for an improved European Union," he said.
Jean-Claude Juncker, president of the European Commission, has said he would work constructively with the new UK government.
Speaking at Labour's London headquarters, Mr Miliband said he had phoned Mr Cameron to congratulate him on his victory.
He said he would step down as leader with immediate effect after Labour won 26 fewer seats than in 2010, adding that deputy leader Harriet Harman would succeed him pending a leadership contest.
Labour, he said, needed an "open and honest debate about the way forward without constraints".
"I am truly sorry that I did not succeed," he told party supporters. "I have done my best for nearly five years."
He added: "Britain needs a strong Labour Party. Britain needs a Labour Party that can rebuild after this defeat. We have come back before and we will come back again."
Announcing his own exit as leader after more than seven years, Mr Clegg said the results - which saw his party reduced from 57 to eight seats - were the most "crushing blow" to the Liberal Democrats since they were formed in the late 1980s.
"This is a very dark hour for our party," he told party supporters in London. "But we cannot and we will not allow the values of liberalism to be extinguished overnight. Our party will come back. Our party will win again."
Mr Cameron has been congratulated on his victory by a number of foreign leaders.
In a statement, Prime Minister John Key said he hoped to speak with his UK counterpart by phone in the next few days and would also write to him formally on behalf of the New Zealand Government.
He said there were strong trade and economic links between the two countries, as well as cultural ties, and he looked forward to working with Mr Cameron over the coming years.
An independent inquiry is to look at the accuracy of UK election polls, after they failed to predict the Conservatives' lead over Labour.