Gordon Brown said the agreement came before the restaurant meeting
Gordon Brown has admitted he struck a deal with Tony Blair over the 1994 succession to the Labour leadership.
He said they agreed Mr Blair would have a clear run, and then support Mr Brown to take over when he stepped down.
But he told ITV1's Piers Morgan's Life Stories the deal was not made at the Granita restaurant as widely believed.
The prime minister also wept when he spoke about his daughter Jennifer, who died aged 10 days after suffering a brain haemorrhage in 2002.
The so-called Granita pact - named after the restaurant in Islington, north London - has been the subject of intense speculation.
Ben Wright, BBC political correspondent:
It is certainly a contrast to the growling Gordon Brown who machine-guns statistics at his opponents from the despatch box and calls for politics to be a contest about policy.
The Piers Morgan interview (sympathetic questions from a friend of the PM) presented Gordon Brown with a chance to bare his soul in a way he has not done before.
I am told firmly by sources close to Mr Brown that he did not contrive to deliver such an emotionally charged interview. But they say the interview is a good reflection of him and his character.
Mr Brown has always been reluctant to make his private life public and his sons Fraser and John remain far away from the spotlight. But with an election weeks away, Mr Brown now says it is important for people to know who he is.
David Cameron has always been more comfortable with this approach.
But whether Gordon Brown likes it or not, the personalities and life stories of the party leaders will play a part in the choice voters make when they go to the polls.
Mr Brown succeeded Mr Blair as Labour leader, and prime minister, in June 2007.
Filmed in front of an audience, Mr Brown told the programme: "There was no deal struck at Granita's. That's been one of the great myths and people have written about it."
He added: "I'd already agreed with Tony before that dinner that he would stand for the leadership and I would stay on as the shadow chancellor, as the person in charge of economic policy.
"And there's an understanding that at some point Tony would stand down and he would support me if, when, that was the case. And that's where we left it."
At the time of Labour leader John Smith's death in 1994, Mr Brown was shadow chancellor and Mr Blair was shadow home secretary.
The two were close political allies but Mr Brown was seen as the senior figure and it was assumed he would run for the leadership.
Neither man has spoken before about the terms of any deal or even if one existed.
Tony Blair was seen as the junior partner to Gordon Brown in 1994
Asked by Piers Morgan if he believed he would be Labour leader after Mr Smith's death, Mr Brown says: "I thought that would be possible and the first person I phoned when I heard John had died was Tony.
"And I said: 'Look, Tony, you may not know this but despite the fact it's not been announced, John unfortunately has, has died.' So I was talking to Tony, I said, 'Look, we've got to sort this out,' And so we started a conversation."
He added: "I believed I could do the job, I believed that I'd got the experience and built up the experience to do it."
'Modern love story'
He told the programme, to be broadcast on Sunday, there were fierce battles between himself and Mr Blair during their time in government together as chancellor and prime minister.
But he insisted the relationship between the holders of those two jobs would be "incredibly difficult, even if you are friends".
In a wide-ranging interview, weeks ahead of an expected general election, Mr Brown also paid glowing tribute to his wife Sarah.
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"Sarah and I, we're, we're a modern love story. We have been very fortunate. She is beautiful, she's elegant, she's compassionate, she's dignified, I'm very, very proud of her."
The prime minister also described emotionally the moments when he knew his newborn daughter would not survive.
He said: "And I could hold her hand and I could feel that she knew I was there and there was nothing that you could see that was actually wrong, but she just wasn't growing.
"And then probably after a week Sarah and I... she was in the special care. I turned to the doctor and I said: 'She's not going to live, is she?'
"And he said: 'No, I don't think so. She's not going to live'."
Mr Brown has previously been reluctant to speak publicly about his family but this is the second interview in a week in which he has touched on the subject.
Chancellor Alistair Darling told the BBC: "What you are seeing is a highly personal view of Gordon, people want to know a bit more about politicians than perhaps they did in the past, so it's good, people can see what he's got to say."
Watch the whole interview on Piers Morgan's Life Stories: Gordon Brown, on Sunday 14 February at 1015 GMT on ITV1.