Sinclair, 57, takes over from Matt Eastwood, who is being moved to New York to run the agency's operation in the US as its chairman and creative director.
Sinclair was the first creative hired by the Saatchi brothers in 1970 and is responsible for seminal work including the "pregnant man" ad for the Department of Health.
A Saatchi lifer, Sinclair's appointment to the creative helm is seen as an attempt to replicate the creative success that made the agency famous.
Moray Maclennan, the M&C Saatchi joint chief executive, said: "Jeremy Sinclair has always been the keeper of M&C Saatchi's creative flame. He has a very clear idea of the creative work he wants the agency to be producing."
Credited with "having a way of turning Charles Saatchi's wildest ideas into reality without filtering out their energy", Sinclair was also responsible for writing the agency's national press ads when it launched with the strapline: "Why I think it's time for a new kind of agency."
Most recently, he worked on the "I believe" creed for the Conservative party leader, Michael Howard, that ran in The Times.
The move sees Eastwood, whose career at M&C Saatchi started eight years ago in Melbourne, returning to New York after a 20-month stint in London.
He was promoted to creative director in London a year ago. The title was part of a package rapidly put together by M&C Saatchi to prevent Eastwood from accepting an offer to be the executive creative director at Grey.
M&C Saatchi's New York operation has a staff of 20, focused primarily on servicing the agency's British Airways account. Eastwood will work with the chief executive, Robert Fletcher. He will also have a role in the small Los Angeles operation. He takes up the new role on 5 April.
Eastwood said: "I felt like I left New York too early. This is a good opportunity for us that we never really exploited. I can go back and finish what I started."
During his reign, the agency's creative highlights include work for Lucozade's Sport Hydro Active, the Silk Cut swan-song ad featuring a fat lady singing and the Foster's head tap campaign.
In London, Tiger Savage remains as the head of art and Simon Dicketts continues in the role of executive creative director. James Lowther is the agency's chairman.
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