Bainbridge, the former director of marketing, communications and audiences for the Future Media & Technology division at the BBC, will work alongside Helen Calcraft, MCBD's chief executive.
Jeremy Miles, its chairman, who is expected back soon after illness, will return to the agency on a part-time basis.
The appointment does not affect Jonathan Durden, a MCBD partner, who has an advisory role at the agency.
Bainbridge, who was responsible for the launch of the BBC iPlayer, started his career at BMP DDB Needham before moving to five in 1996 for its launch. He later became five's deputy marketing director. In 2002, he left to set up the digital agency Whoosh, before joining the BBC in 2006.
Calcraft said: "David is a unique talent with a unique set of skills to bring to our agency."