Palmer, the global planning director on Smirnoff at BBH, will replace Bobby Hui, who has been promoted to international planning director.
In his new role, Palmer will report to the chief strategy officer, Chris Chalk. He will be responsible for leading and developing Saatchi & Saatchi's strategy department in the UK.
Palmer joined BBH in 1998 as a planner. He was appointed to the board in 2000, before being promoted to his current role the same year. He has previously worked at TBWA GGT Simons Palmer and BDH Manchester.
Chalk said: "We have a great community of planners here and with Matthew's leadership, we'll make the most of it."