Channel 4 has signed a three-year deal with Love Productions, the producer of the show, which said it had been keen to remain on free-to-air TV.
The cooking contest has grown into a ratings monster for BBC One, attracting more than 13 million viewers for its final last year, since making its debut on BBC Two with a 2011 series watched by 2.5 milllion people.
Channel 4 said the first Bake Off programming it plans to air, in 2017, is a celebrity version in aid of Stand Up to Cancer.
The BBC tried to keep Bake Off with an offer of £15m over three years but Love Productions believed its value was above £20m and was also concerned by the limited platform offered by the BBC for content related to the show, according to The Guardian.
It is not clear how much Channel 4 has paid for the series and it is also uncertain whether the presenters, Sue Perkins and Mel Giedroyc, and judges, Mary Berry and Paul Hollywood, will remain with the show although the producers and Channel 4 are sure to want to keep them.
Media agency buyers welcomed the move. Dominic Williams, chief trading officer at Denstu Aegis Network’s Amplifi, said: "I think the Channel 4 move will give clients another great opportunity to sponsor an amazing show.
"Thirteen million watch Bake Off and it can only get better as Paul and Mary have got the format spot on. It’ll be another great vehicle for brand. We will be definitely be recommending it to our clients. I can't believe the BBC has lost it."