Gerster replaces Lou Shultz, who announced his retirement in January. Gerster's role will centre on expanding Initiative's network of 85 offices. He joins on 22 April and will report directly to David Bell, the vice-chairman of Interpublic.
The appointment of Gerster will bolster Initiative's management in the US. Forissier will continue to be based at Initiative's Paris HQ.
Gerster is replaced at MediaCom by Alexander Schmidt-Vogel, the current chief operating officer.
The company has also promoted Dene Callas and Jon Mandel, its joint managing directors, to the roles of joint chief executives of its US operations.
As the head of Grey's media services division, Gerster led its MediaCom unit when it split media out of its advertising agency offering in the late 80s. In joining Initiative, which has billings of more than $20 billion, he is taking on a role with a media network that is almost twice the size of MediaCom.
Gerster said: "I am looking forward to applying my experience in the media business on a global scale. Initiative Worldwide is a leading name internationally."