Conservative leader David Cameron is to form a government and is now the new British Prime Minister.
Watch | Read David Cameron's speech
The new prime minister said he aimed to form a full coalition government between his Conservative party and the smaller Liberal Democrats party.
'I aim to form a proper and full coalition between the Conservatives and the Liberal Democrats,' he told reporters.
'I believe that it (is) the right way to provide this country with the strong, the stable, the good and decent government we need so badly.'
Gordon Brown earlier resigned as prime minister, bringing 13 years of New Labour government to an end.
Watch | Read Mr Brown's resignation speech
Mr Brown tendered his resignation to Queen Elizabeth, making way for a new power-sharing government led by Mr Cameron to be formed.
Mr Brown and his wife spent over 15 minutes at Buckingham Palace - where he travelled after announcing his resignation outside 10 Downing Street.
A statement issued by Buckingham Palace afterwards said the queen had accepted his resignation.
The Conservatives won 306 seats in last week's election - 20 short of a clear majority of 326. They were followed by Labour on 258 and the Lib Dems on 57.
The Conservatives and Lib Dems initially held talks on a power-sharing deal before Gordon Brown offered to quit yesterday.
Labour had failed to strike a deal with the Liberal Democrats.
Taoiseach Brian Cowen congratulated Mr Cameron on his
appointment as British Prime Minister.
He said: 'I send my warm congratulations to David Cameron on his appointment as British Prime Minister.
'I look forward to meeting with him to discuss future relations between Ireland and Britain, in all their dimensions, to build on the great achievements of the peace process in Northern Ireland and to help tackle the enormous challenges now faced by Europe and the world.
'I wish Mr Cameron all the best as he takes on the challenges and
opportunities that now arise with these new responsibilities.'
Cameron's Cabinet
Downing Street said no ministerial posts would be officially confirmed yet but reports suggested the deal struck between David Cameron and Nick Clegg's parties includes a promise of six seats around the Cabinet table for the Liberal Democrats.
George Osborne is tipped to become the youngest Chancellor of the Exchequer, while William Hague will be Britain's new foreign secretary.
Mr Clegg himself is to be rewarded for leading his party to a share of power with the post of Deputy Prime Minister.
It is expected that Vince Cable will be appointed Mr Osborne's number two as Chief Secretary to the Treasury.
Reports suggested Liberal Democrat David Laws will be made Schools Secretary.
Tory Liam Fox was also reportedly given the post of Defence Secretary, retaining his role held in the shadow cabinet.
The need to give jobs to Liberal Democrats means some members of Mr Cameron's shadow cabinet are likely to be awarded less senior jobs.
