Fincham will replace outgoing controller Lorraine Hegessey, who is leaving the BBC to take his old job at Talkback Thames.
He will be responsible for the corporation's editorial vision, commissioning and scheduling strategies and working closely with the team of commissioners and channel controllers.
Fincham joined Talkback in 1985 when it was a radio, commercials and corporate video company set up by Mel Smith and Griff Rhys Jones. In 1986, he became managing director and in 1989 he led the company's move into television production.
He has been responsible for some of the biggest shows on TV over the last decade including 'I'm Alan Partridge', 'Jamie's Kitchen' and 'The Lost Prince', the award-winning drama by Stephen Poliakoff.
Jana Bennett, BBC director of television, said: "If there are maybe 10 people who have shaped television over the last decade, Peter is one of them.
"He is known as someone who attracts the best talent, supports the best ideas and then backs them with a tenacious passion."
The decision is likely to ruffle a few feathers at the BBC as three internal applicants -- daytime controller Alison Sharman, head of drama commissioning Jane Tranter, and BBC Three controller Stuart Murphy -- were tipped to take the top job.
Fincham said of the new role: "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."
Heggessey announced she was leaving the BBC in January. She has spent five years at the corporation and was responsible for commissioning hits such as 'Blue Planet', 'Spooks', 'State of Play' and 'Strictly Come Dancing'.
Fincham will take over the job this summer.
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