Joining in the summer, Fincham will take over from Lorraine Heggessey, who has effectively swapped roles with the former chief executive of production house TalkBackThames.
Fincham has been seen is one of the most qualified figures in the business for producing both innovative and populist programming, after victories with Jamie’s Kitchen, House Doctor and Grand Designs, plus ITV1’s reality pop shows and the BBC’s They Think It’s All Over and I’m Alan Partridge.
The outgoing chief executive of TalkBackThames will report to the BBC’s director of television Jana Bennett and his brief will cover BBC One’s editorial vision, commissioning and scheduling.
Bennett said: "If there are maybe 10 people who have shaped television over the last decade, Peter is one of them.
"He has a formidable track record in delivering original and outstanding programmes across a range of modern public service genres, and the knack of making them appeal to broad audiences. “
The announcement ends a turbulent week at the BBC after director-general Mark Thompson unveiled the latest round of job cuts, bringing the total so far up to 3,800.
Thompson has also been the subject of a bizarre story brewing in the national press over an alleged incident with a producer in his former sting at the corporation.
Fincham said: "I grew up watching BBC One and the first programmes I made as an independent producer were for BBC One, so it's enormously flattering to be asked to take over as channel controller from Lorraine Heggessey.
"I am used to being responsible for a wide range of programmes and BBC One stands for range, quality and integrity. It also has a unique breadth of appeal.
"The BBC is going through big changes, but BBC One remains its flagship channel and reinterpreting and reinvigorating it for new audiences is about as exciting a challenge as it gets.
By Kevin May
Fincham unveiled as controller of BBC One
The BBC has appointed Peter Fincham, the man behind such ITV success stories as The X Factor, Pop Idol and The Bill, as the new controller of BBC One.