Benjamin Netanyahu announced the appointment today.
Cohen will replace Tamir Pardo, who leaves the post next month.
Cohen is a veteran Mossad agent who has served as deputy director.
He also led Tzomet, the department that directs field agents.
Netanyahu pointed to Iran and the Islamic State group as two of the main threats facing the region and the world.
He said Mossad agents operate around the clock with "exceptional daring, great imagination and sometimes with personal risk" to ensure Israel's security.