Tarrant, who has spent 17 years hosting the show on 95.8 Capital FM, will move aside for Vaughan early next year.
Vaughan is currently contracted to the BBC but this deal, which involves his own TV chat show Johnny Vaughan Tonight, ends next year. The show has failed to bring in large audiences.
Tarrant is contracted to work on the Capital Breakfast Show until the end of 2003 and reports have suggested that he will host an afternoon spot for the station.
Capital has acted to replace Tarrant to avoid the kind of damaging speculation it suffered last year when doubts over Tarrant's future undermined the company's image in the City.
Vaughan, 37, has signed a three-year deal from spring 2004 to present the show, which attracts 1.65 million London listeners.
Tarrant said: "I think Johnny is a great choice as my successor and he'll bring a lot to the show. The Big Breakfast showed that he's vibrant, lively, funny and exciting in the mornings and I'm sure he can bring all this to the Capital Breakfast Show."
Capital's decision to hire Vaughan follows the announcement of a series of changes by Capital FM's managing director, Keith Pringle. These include a revamp of its weekly and evening schedules.
Pringle said: "Johnny has perfect credentials for the job; he's funny and spontaneous and most importantly a real London guy who fits in perfectly with how our listeners want to be."
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