Sue Perkins and Mel Giedroyc will step down as hosts of The Great British Bake Off when it moves to Channel 4.
The duo have fronted the show since it began on BBC Two in 2010, alongside judges Mary Berry and Paul Hollywood.
They said in a statement: "We made no secret of our desire for the show to remain where it was... we're not going with the dough."
Love Productions, which makes the show, thanked them for "bringing their unique humour to the tent".
'Rise and rise'
Giedroyc and Perkins said they were "very shocked and saddened" to learn Bake Off will be leaving the BBC.
Their statement continued: "The BBC nurtured the show from its infancy and helped give it its distinctive warmth and charm, growing it from an audience of two million to nearly 15 [million] at its peak.
"We've had the most amazing time on Bake Off, and have loved seeing it rise and rise like a pair of yeasted Latvian baps.
"We're not going with the dough. We wish all the future bakers every success."
In their statement, Love Productions said: "We would like to thank Mel and Sue for bringing their own unique humour to the tent over the past years and we respect their decision not to be part of the Bake Off team on Channel 4."
A spokesman for Channel 4 said earlier today that it "would be delighted if the presenters and judges want to come to Channel 4".
It is not yet known if judges Mary Berry and Paul Hollywood will stay with the show.
'Joy of Mel and Sue'
The BBC fell £10m short of the amount of money required to keep The Great British Bake Off, BBC News understands.
The corporation is thought to have offered £15m per year to keep the programme on the BBC.
That would have been double the amount the BBC currently pays for the show and its sister programmes such as An Extra Slice and the Sport Relief specials.
But it is understood Love Productions refused to entertain any offers below £25m per year.
Channel 4 will begin airing the programme in 2017, starting with a celebrity special in aid of Stand Up To Cancer.
On the news that Giedroyc and Perkins were leaving, former contestant Kate Henry, who was on the show in 2014, told the BBC News channel: "I'm quite sad that future contestants won't get to experience the joy of Mel and Sue in the tent.
"They really make it a fun experience rather than painfully stressful."
She said it would be an "utterly different show" if Berry and Hollywood were also to leave.
Ian Cumming, who was a contestant last year, told the BBC: "I'm really shocked. You're losing the humour of the show (with Giedroyc and Perkins leaving). That was always its charm. I think it will gradually slip down but we'll see."
Richard Burr, a finalist on series five in 2014, tweeted: "Without Mel and Sue it just isn't Bake Off. @Channel4 has just bought a tent."
John Waite, who won the third series of Bake Off, tweeted that he "was not feeling so hopeful" now Giedroyc and Perkins had left.
Both Giedroyc and Perkins have had plenty of work outside the Bake Off tent.
The pair started on Channel 4 in the 90s with daytime TV show Light Lunch, when their on-screen chemistry and ad-libbing became a popular staple with students and daytime TV viewers.
Giedroyc has co-presented the BBC's Eurovision semi-finals in Stockholm and Eurovison You Decide, as well as the BBC One's The Gift with Matt Baker, a show reuniting people who wanted to say thank you or sorry. She also took to the stage to play housekeeper Frau Schmidt in ITV's live Sound of Music last year.
Perkins has hosted BBC Two panel show Insert Name Here as well as shows with Giles Coren, including BBC Four's Edwardian Supersize Me and BBC Two's The Supersizers Go. She also wrote and starred in BBC Two sitcom Heading Out, set in a vet's surgery, in 2013.
Her work also includes presenting Thronecast on Sky Atlantic, the companion show to the hugely popular Game of Thrones TV series.
TV host and actor James Corden tweeted "huge respect" for the departing presenters, while Youtube vlogger Zoella said the show wouldn't be the same.
Guardian writer Charlotte Higgins tweeted: "Mel and Sue completely essential to #GBBO success."
The Sun's Dan Wootton described Giedroyc and Perkins's departure as a "huge blow".
But Telegraph columnist Neil Midgeley said the BBC should have paid out £25m to keep the show.
"The BBC didn't have to lose its biggest hit, The Great British Bake Off, to Channel 4. For BBC director-general Lord Tony Hall, who is constantly fighting off accusations of financial largesse from Tory MPs, it was a splurge too far.
"But, regardless of the politics, this is one BBC cheque that Lord Hall will come to wish he had written."
The shows and presenters that have swapped channels
- The Great British Bake Off - BBC to Channel 4 (2016)
- British Horse Racing - Channel 4 to ITV (2017)
- The Voice - BBC to ITV (2017)
- Formula One - BBC to Channel 4 (2016)
- Birds of a Feather - BBC to ITV (2014)
- Big Brother - Channel 4 to Channel 5 (2011)
- Jonathan Ross - BBC to ITV (2011)
- Christine Bleakley & Adrian Chiles - BBC to ITV (2010)
- Neighbours - BBC to Channel 5 (2007)
- Graham Norton - Channel 4 to BBC (2005)
- University Challenge - ITV to BBC (1994)
Love Productions, which makes the programme, said negotiations with the BBC had been taking place for a year, with a last-ditch meeting on Monday.
Richard McKerrow, Love Productions' creative director, said the firm had found "the perfect new home for Bake Off" at Channel 4.
Scott Bryan, TV editor of Buzzfeed UK said: "You can't find any bigger a slot or do any better in terms of viewers than where it already is - on BBC One in a main teatime evening slot.
"Channel 4 would be monumentally thrilled with the idea that they have the same ratings that it has on BBC.
"I feel they would be equally happy if it got a few million less, because that would still be a few million more than another programme they would have on that slot, so it's still a massive win for them."
It is not yet clear what time slot the show will have on Channel 4 or whether it will be cut or extended in length.
Bake Off was 2015's most-watched programme, with 15.1 million viewers for the final, according to consolidated figures which include catch-up viewing.
The seventh series is currently being shown on BBC One on Wednesday evenings. More than 10 million tuned in for the opening episode.