Mark Goodwin, Jason Lawes and Sam Ball will continue as creative directors – the most senior role in the agency’s creative department.
Bedwood, a founder of Lean Mean Fighting Machine, which is now part of M&C Saatchi, is departing in June to start a health business with his wife.
Tom Bazeley, the chief executive of M&C Saatchi and a founder of LMFM, said: "I’ve worked with Dave since the turn of the century and couldn’t imagine a better bloke to go in to bat with.
"He’s always had an entrepreneurial fidget to him and so it’s no great surprise that he’s leaving to pursue his dream of designing and launching a new product. Of course, I’m secretly hoping it fails and he comes back to agency land soon."
Bedwood has led the creative department with Goodwin, Lawes and Ball, another founder of LMFM, since the departure of the executive creative director, Elspeth Lynn, in January.
He said: "I’ve done many stupid things in my career but leaving true friends, great clients and an earn-out to work on a product idea my wife has had… well, let’s say it’s right up there."
M&C Saatchi bought LMFM last year and the digital shop has since been integrated into the main agency.
Bazeley has been the chief executive of M&C Saatchi since October 2014, when Camilla Harrisson left to join Anomaly.