Tony Blair has said he expects "in all probability" that Chancellor Gordon Brown will succeed him as prime minister "in the next few weeks".
Is Mr Blair ready to hand over the baton to Mr Brown?
Mr Blair says he will announce his resignation next week, after which he will stay as PM for about seven weeks until Labour chooses his successor.
He has so far refused to formally endorse Mr Brown as the next PM.
He made his prediction while campaigning in Scotland on the 10th anniversary of being elected to power.
Mr Brown, who helped create New Labour with Mr Blair, is not now expected to face a high level challenge for the leadership.
Mr Blair has said he will leave No 10 by September, but there has been speculation about the precise timing of his departure.
There had been predictions he would use his 10th anniversary to announce he was stepping down.
But he moved, earlier on Tuesday, to dampen that speculation, telling GMTV: "I'll make my position clear next week, I'll say something definitive then."
But later on Tuesday morning he used an election rally instead to suggest Mr Brown would be his successor within a matter of weeks.
He told party workers: "In all probability a Scot will become prime minister of the United Kingdom, someone who has built our economy into one of the strongest in the world, and who, as I have said many times before, would make a great prime minister for Britain."
Mr Blair would not be drawn on which day next week, which includes a Bank Holiday Monday, his official resignation statement would be made.
Speculation has focused on Wednesday or Thursday, after the planned resumption of power sharing in Northern Ireland - seen as one of the biggest achievements of Mr Blair's time in office.
According to press reports, Mr Blair will use his retirement announcement to formally endorse Mr Brown's leadership bid - in a final act of reconciliation with the chancellor, with whom he has enjoyed a stormy relationship.
Mr Brown has, meanwhile, heaped praise on Mr Blair in an article to mark his 10 years in power.
Writing in The Sun newspaper, Mr Brown said he was "honoured" to call Mr Blair his "oldest friend in politics", while admitting there had been "ups and downs" along the way.
He praises Mr Blair for standing shoulder to shoulder with America after the 11 September attacks, for bringing the 2012 Olympics to London, his role in the Northern Ireland peace process and his handling of the death of Diana, Princess of Wales.
And - in a further sign of an impending Brown coronation - EU Trade Commissioner and key Blair ally Peter Mandelson predicted the chancellor would succeed Mr Blair in Number 10.
"In all probability, Gordon Brown will follow Tony Blair. He will now have been able to fulfil his ambition and his desire to lead the party and be prime minister," he said.
Mr Mandelson, who was one of the key architects of New Labour, also admitted the party focused too much on media management during its first years in office.
The former Northern Ireland secretary said it was not until late in the first term that Mr Blair concentrated more on policies.
"We were perhaps too ready to place emphasis on our management of the media in those early years of government, rather than concentrate on a more policy driven process," said Mr Mandelson.
He added: "I acknowledge it, but I think it was put right after the first few years. "
The prospect of a Cabinet-level challenge to Mr Brown has all but disappeared but he could still face a contest with either John McDonnell or Michael Meacher from the left of the party.
In a speech earlier, Mr Blair said 10 years of Labour government have left the UK stronger, fairer and better.
But Conservative Leader David Cameron, giving his reaction to Mr Blair's 10th anniversary, said: "Tony Blair's time as prime minister started with great hope but has ended with disappointment.
"Tony Blair will be remembered as a successful party leader but not as a good prime minister."
Lib Dem leader Sir Menzies Campbell said: "I would give him four out of 10 for the performance of this government, considering all the hope there was. In the last five years they have been a disappointment."
He added: "Whatever else were Mr Blair achievements... Iraq will follow him into retirement."
On the prospect of a Brown premiership, Sir Menzies said: "People are waiting with some apprehension to see whether he will be a genuinely reforming prime minister, or whether what he does will be subject to the same media manipulation as the Blair government."