Gordon Brown "never fully reconciled" himself to Tony Blair becoming Labour leader instead of him in 1994, Peter Mandelson has told BBC News.
Mr Mandelson: Mr Blair had something Mr Brown "wanted so much"
Mr Mandelson said the chancellor's feelings at "losing something he wanted so much" had created a "fissure" in the New Labour family from the start.
But he now recognised that Mr Blair had been a successful PM, he said.
His comments came as Mr Blair prepared to make his farewell speech as leader to the Labour Party conference.
It is the first time Mr Mandelson, now a European commissioner, has spoken so candidly about the deal which saw Mr Brown give up his bid to become Labour leader to give Mr Blair a clear run.
The widespread assumption is that the deal also included a promise from Mr Blair that he would hand over at some future time to Mr Brown.
Tensions over when Mr Blair might stand down - and whether or not he endorses Mr Brown as his successor - have dominated this year's Labour conference in Manchester despite efforts to present a united front.
Mr Blair is expected to pay tribute to the chancellor during what he has said will be his last conference speech as prime minister at about 1415 BST on Tuesday.
But he is also expected to stop short of explicitly backing him as the man to take Labour forward.
Mr Brown used his speech to the conference on Monday to admit he and Mr Blair had had differences over the years, but also to say it had been "a privilege" to work with him.
But that olive branch was largely undermined by the report that Cherie Blair was overheard describing those words as "a lie".
She later denied making the comment and Mr Mandelson called the row "mediatrix... a storm in an egg cup".
Mr Mandelson was Labour's director of communications when former Labour leader John Smith died and is still a close confidant of Mr Blair.
He said a "deep breach" had opened up between him and Mr Brown when he had backed Mr Blair to come the new leader.
Cherie Blair's reported comments overshadowed the conference
"Within the party, or more strictly within the New Labour family, there has been a fissure really from the word go," he told BBC Radio 4's Today programme.
"And the reason for that is that Gordon thought that he could and should have been leader in 1994.
"He believed that he should have succeeded John Smith and he's never fully reconciled himself to not doing so."
Mr Mandelson said Mr Brown, despite his feelings at losing the leadership, had recognised "that actually Tony has done very well".
"For all the regrets that he might have had that he was not leader and prime minister himself during this period, I think he does recognise Tony Blair's qualities and I think that is entirely reciprocated from Tony Blair to Gordon Brown," he said.
Mr Blair would see his greatest legacy as seeing a successor taking the party to a fourth election victory on a New Labour platform, argued Mr Mandelson.
The prime minister wanted whoever it was to be, if anything, stronger than him and more modernising than him. And he saw those qualities in Mr Brown, said Mr Mandelson.
"Should Gordon Brown be the one to succeed him he will want Gordon Brown to succeed as leader and as prime minister and he will want him to be re-elected and he will work for that," he said.
"There's no sense in Tony's mind ...you know, I was the golden years and now the fallow times must follow. He doesn't feel like that at all."
Mr Mandelson also said Mr Brown would be able to defeat David Cameron at an election: "I do think he is a winner. He has got a very solid body of beliefs. There is nothing surface or superficial about Gordon Brown. He has real depth and I think people want to see that in their nation's leader."
Former Home Secretary Charles Clarke said on Monday he did not regret his attack on Mr Brown, when he called him a "control freak".
Mr Mandelson said Mr Clarke had spoken frankly but had not given the whole picture of Mr Brown.
Mr Mandelson says Mr Brown's strength comes through his flaws
"The chancellor might have all sorts of flaws but his inner strength as a politician came through," he said.
He said Mr Brown's speech had indicated he wanted to be a more inclusive figure in future.
"What I heard was a coming to terms with the need to change to a more collaborative and unifying style if he became leader of the party," said Mr Mandelson.
Mr Brown had to embrace the idea of inclusiveness in private and in public if Labour's different tributes were to be welded together, argued Mr Mandelson.