The Labour leader has hailed his election landslide as an "historic moment" and is expected to announce his new cabinet later in the day.
The Liberal Democrats gained seven seats as well as increasing their share of the national vote, a success which leader Charles Kennedy said would help them take a share of government by the end of the decade.
Mr Blair arrived at Labour headquarters in London at 0543 BST where he was greeted by flagwaving supporters including singer Mick Hucknell and former EastEnders star Ross Kemp, ministers and party workers.
"Our mandate is to carry on the work we have started," he told the cheering crowd.
"It is indeed a night of history for our party."
Mr Hague congratulated Mr Blair by telephone at around 0315 BST on Friday.
Speaking later, he said: "We must respect the verdict of the voters and listen to what they have said."
Labour's landslide comes, however, against the backdrop of the lowest voter turnout since 1918. The figure is being put at under 60%, down from 71% in 1997.
Labour has a net loss so far of just six seats.
At a glance
The far-right British National Party stunned political observers when it took more than 11,000 votes across the two Oldham constituencies, the scene of recent race riots.
At the count in Oldham West and Royton, where BNP leader Nick Griffen came third to Labour and the Tories, candidates were banned from making speeches for fear of sparking racial hatred.
Outside Labour's Millbank offices in London Mr Blair said: "The one thing we have to remember is that now is the time when the people of this country want us to serve them, and want us to do the things we promised to do."
He said that he would build on the foundations of economic stability created by "brilliant" Chancellor Gordon Brown, who also co-ordinated Labour's election campaign.
With all results in from England, Wales and Scotland the next parliament will see Labour return 413 MPs, the Conservatives 166, Lib Dems 52 and other parties 10.
Results are still coming in from Northern Ireland but the final overall majority for Labour will be 167 compared to 179 after the 1997 election.
Hague steps down
In a dramatic statement outside Conservative Central Office in London, Mr Hague said he would stand down as soon as a successor had been chosen.
"No man is indispensible. No man is more important than the party," he said.
"It is vital for leaders to listen and parties to change. I believe it is vital the party be given the chance to choose a leader who can build on my work, but also take new initiatives and hopefully command a larger personal following in the country.
"I've therefore decided to step down as leader of the Conservative party when a successor can be elected in the coming months."
Earlier, the Tory campaign has come under fire from former ministers.
Lord Brittan said the decision to focus on Europe and asylum seekers was a "huge strategic misjudgement".
This, he said, had made the Tories look "shrill and extremist".
Pro-European Tory backbencher Ian Taylor said his party had campaigned on the "wrong strategy".
Shadow chancellor Michael Portillo described the result as disappointing but called for a period of reflection.
He paid tribute to William Hague and appealed to Tory party members not to "say anything hasty" which they may regret later.
Charles Kennedy returned to his party's London HQ and told party workers they must seize the mantle of opposition from the Tories and campaign in the next parliament for better public services.
He said the party would now have to work harder as its increased electoral strength would mean it would be under more scrutiny than ever before.
"We are the party of the future and this decade can see us as a party of governance in this country," Mr Kennedy declared