The Labour leader, now back in Downing Street, has hailed the election landslide as an "historic moment".
Liberal Democrat leader Charles Kennedy hailed his party's "remarkable achievement" building on their record success in 1997.
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 shortly after 0300 BST on Friday.
Speaking later, he said: "We must respect the verdict of the voters and listen to what they have said."
Mr Blair will go to Buckingham Palace later on Friday after which he is expected to announce a cabinet reshuffle.
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.
The Tories have recorded a net gain of one seat.
The Lib Dems have a net gain of four seats.
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.
Mr Blair, speaking at his own count, said: "There's no greater honour than to serve you as prime minister.
"And you have given us tonight an historic moment for the Labour Party.
At a glance
"It's an extraordinary thing."
The latest BBC forecast of the final result is for Labour to have 414 MPs, the Conservatives to have 167, the Liberal Democrats 52, with 26 for other parties.
At the 1997 general election Labour had 418 MPs, William Hague's Tories had 165 and Charles Kennedy's Liberal Democrats had 46.
William Hague said the Tories would reflect on the result and he will set out his views later on Friday.
But he said the low voter turnout was a "sobering lesson" for all the parties.
"The Tories must review, redouble and intensify their efforts to provide an alternative government," he said.
However, 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".
He said Mr Hague would have to "make his own mind up" about his future as party leader.
Former minister Rod Richards called on Mr Hague to resign after describing the party's campaign a "catastrophe".
Party chairman Michael Ancram congratulated Labour and praised William Hague's leadership of the campaign.
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.
Lib Dem success
Charles Kennedy said the Liberal Democrats had "built on the amazing breakthroughs of four years ago".
He added: "We have taken ourselves further forward across Britain as a whole and we are very much the party of the future for British politics. I think those politics will be better as a result."
Mr Kennedy, who congratulated Tony Blair on winning the election, said his party would seek to provide a "relevant and responsible" opposition into the next parliament.