In response, BBC Magazines has appointed Sara Cremer, currently the executive editor of new product development at Emap Elan, as the editor of Eve.
Bruton, who also edited the BBC's quarterly What to Wear fashion magazine, will take up the Emap position at the end of this month and will work closely with Fiona McIntosh, the recently appointed editor-in-chief.
Bruton will build the team behind Emap's biggest ever launch, which is backed by a £16 million marketing spend.
Cremer will join Jessica Gibson, who has been promoted from associate publisher of Eve to publisher of the title. Cremer is also due to join the magazine at the end of November.
Before Eve, Bruton edited IPC Media's Living etc.
McIntosh said: "Jane's reputation across the publishing industry and, in particular, her achievements at Eve and Living etc, put her at the top of our wish list when it came to searching for an editor for Grazia."