The broadcaster, who currently presents the station's mid-morning phone-in programme, will make the change on January 4, 2016, reported Digital Spy.
Feltz said, "I am bubbling over with excitement at the opportunity to present the BBC Radio London breakfast show and I hope my lovely listeners will be up bright and early to enjoy the thrills and spills of this brand new programme."
BBC Radio London's editor David Robey said: "Vanessa is one of the biggest names in radio with her programmes on BBC Radio London and BBC Radio 2 so I'm delighted even more listeners can now hear her at Breakfast setting London's news agenda as they wake.
Current "Breakfast Show" hosts Penny Smith and Paul Ross will move to BBC Radio 2 and BBC Radio Berkshire respectively when Feltz takes over.