Sky, in conjunction with Princess Productions, was among four companies shortlisted for the contract, among them incumbent Planet 24 and Talkback Productions, which produces Brass Eye and They Think it's All Over.
The new show, as yet unnamed, will occupy the slot between 7am and 9am on weekdays. It will include a mix of sports, showbusiness and news presented in an appropriate style for a young audience.
Sharon Powers, Channel 4 breakfast editor, said: "We were thrilled with this pilot and felt it was a genuinely distinctive offer at breakfast time."
Channel 4 director of programmes Tim Gardam added: "The Big Breakfast has been one of Channel 4's most distinctive and important programmes for nearly a decade. It represented a breakthrough for TV entertainment as a whole and created a style that has been widely imitated.
"It has also been one of the most successful breeding grounds for new talent, and I would like to thank everyone who has worked so hard on the show over the past nine years."
The final edition of the Planet 24-produced The Big Breakfast will air on 29 March. A start date for the new series has yet to be agreed.
Mark Sharman, director of broadcasting and Production at Sky, said: "We are thrilled to be creating such an important show. Sky and Princess both boast a track record in innovation and pioneering achievement. The success of this bid is a resounding endorsement of Sky's award-winning pool of production talent, and of Princess' leading role as a producer of daily live programmes."
The Big Breakfast was axed in June after a variety of new presenter line-ups failed to attract the impressive audience the show previously enjoyed when it was fronted by Gaby Roslin and Chris Evans, and Denise Van Outen and Johnny Vaughan, who achieved ratings of more than 1m.
The show's audience numbers have now fallen to 300,000. The new show is expected in the spring.
The news of the contract win, however, will please BSkyB-owner Rupert Murdoch, who is slowly beginning to make headway in the terrestrial TV market. Only yesterday, it was announced that Sky News had won the contract to produce Channel 5's early morning news show.
Earlier in the year, a consortium backed by Murdoch failed to win the ITV news contract from ITN, despite seriously undercutting the incumbent's bid.
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