Rebelo will start in his new position in June, reporting to Robert Senior, the UK chief executive of the SSF Group. He will be responsible for the day-to-day running of the London office.
His appointment completes Saatchi & Saatchi London's senior team line-up, following the hirings of Richard Huntington as the head of strategy and Paul Silburn as the creative partner last year.
Senior has been looking for a London head since he took on his SSF role in July. Before that, the agency had been without a chief executive since Lee Daley left in February.
Rebelo said: "Saatchi & Saatchi London is an exciting place to be right now. Robert has put together an astonishing leadership team in Kate (Stanners), Paul and Richard. I have pretty bold ambitions for the agency and look forward to working with Robert and the team to get there."
Senior said: "Michael is world-class talent. He has exactly the right combination of experience, talent and energy to make a colossal difference."
Since joining Saatchi & Saatchi Singapore, Rebelo has led the agency to a number of new-business wins in the Asia-Pacific region including ESPN, MSIG Insurance, Sony Ericsson, Tiger Beer and United Overseas Bank.
Before moving to Singapore, Rebelo was the general manager of Saatchi & Saatchi Australia and held the same role for the agency's New Zealand operation, running the Wellington office.