Bainsfair's responsibilities will include overseeing growth plans, assisting with financial management and pitching for new business. He will work closely with the four founders of LMFM, Tom Bazeley, Dave Cox, Sam Ball and Dave Bedwood.
The appointment comes 12 months after Bainsfair resigned from TBWA after Perry Valkenburg was appointed over his head to the role of European president and worldwide chief operating officer.
Bainsfair was the managing director of Saatchi & Saatchi in 1985 and founded his agency, Bainsfair Sharkey Trott, a year later. BST was later bought by GGT, which merged with the TBWA network in 1998.
Bazeley said: "Lean Mean Fighting Machine is set to benefit hugely from someone who has volumes of experience of running companies with unbelievable success."