Called Tiger's Eye, the venture is a brand and ad consultancy specialising in the luxury beauty and fashion sector.
Savage, probably adland's best-known fashionista, is not planning to recruit staff in the immediate future and claims to have a number of undisclosed clients already signed to the project.
M&C was not clear about how, or if, it would replace her.
Savage trained at the School of Creative Arts, where she was mentored by the late Paul Arden. She then joined Simons Palmer, working on the Nike account, before arriving at Bartle Bogle Hegarty, where she won awards for Levi's and Lynx with her creative partner, Paul Silburn.
After a stint at Leagas Delaney, she was hired by M&C, where she created campaigns for advertisers such as Garrard, Thomas Pink and Vogue.com, as well as overseeing the agency's art direction.
Since that time, she has become something of an advertising brand in her own right, being named Campaign's top adland brand and best dressed in consecutive years.
Savage said: "It's the end of an era for me, and I'm enormously sad to be leaving but it's time for me to do something myself. I've been at M&C for a long time, and learned so much, but I'm looking forward to a new start."
Moray MacLennan, M&C Saatchi Worldwide's chief executive, added: "I'm sad she's going on a personal level, but also on a professional one. Tiger has contributed a huge amount in new-business and creative terms. She has an extraordinary eye and can make anything look amazing."