Tony Blair has admitted there were "disagreements or tensions" with Gordon Brown in his time as prime minister.
Mr Blair stood down as prime minister in June after 10 years
But Mr Blair told the BBC his government had been "infinitely stronger" as a result of Mr Brown's work as chancellor.
He added that he could have "gone on for a little longer" in Downing Street but called his 10 years in power "a long time".
Mr Brown replaced Mr Blair as prime minister in June.
For much of the time since Labour came to power in 1997, there were reports of arguments and power struggles between the two men.
In an interview for The Blair Years, on BBC One, Mr Blair acknowledges there were "real difficulties" in the relationship with Mr Brown, but says there was no "deal" struck for him to step down.
However, he said: "You know when you're prime minister... you're aware that other people may want to succeed you.
"And I always used to say to people, 'it's not an ignoble ambition'. I mean, why shouldn't he want to be prime minister?"
The programme tells the story of how tensions surfaced over Mr Blair's attempts to reform the public health and education services.
It also says Mr Blair made the biggest spending announcement of his time as prime minister - on health spending in early 2000 - without consulting his chancellor.
Former Downing Street adviser Lord Birt reveals that before the 2005 general election he worked on a plan to split up the Treasury and remove Mr Brown from his job.
Lord Birt says Mr Blair and Mr Brown had different policy agendas and that they "clashed".
Former home secretary Charles Clarke tells the programme that Mr Brown had more of a "traditional Labour approach" to public services than Mr Blair.
Interviewed for the programme by Times journalist David Aaronovitch, Mr Blair said: "I'm not hiding the fact there were disagreements or tensions over various issues from time to time.
"Of course, that's what you'd expect. But at the same time, I believe we were infinitely stronger as a government because of his presence there, and because of his achievements.
"It's not that I couldn't have gone on for a little longer. I probably could. But the fact is that 10 years is a long time."
Mr Blair is now the Middle East envoy for the "Quartet" of the United Nations, European Union, Russia and the United States.
He also stepped down as an MP when he resigned as prime minister.
Last week, Mr Blair set up a sporting foundation in his former constituency of Sedgefield, in County Durham.
Part one of the three-part series The Blair Years will be shown on BBC One at 2215 GMT on Sunday.