In 1949, Cohen and his family immigrated to Israel. Cohen married twice. His first wife, Ruth Mense, a pianist for the Israel Philharmonic Orchestra, died from multiple sclerosis in 1988. They had two sons: Ady, a composer, and Sharon, a voice actor and translator. His granddaughter Lenny is also an actress. Cohen's second wife, Da'at Levontin, who he married in the early 1990s, is also a pianist.
Cohen was part of an IDF musical troupe affiliated with the Southern Command. He acted, sang and accompanied himself on the accordion. He left the troupe in 1952 and joined a satirical theatre group.[4]
In 1964, Cohen made his debut film appearance in Sallah Shabati starring Chaim Topol. His other film appearances include the 1969 film Blaumilch Canal directed by Ephraim Kishon and the 2005 film To Take a Wife directed by Ronit and Shlomi Elkabetz. Cohen has also made appearances on television. In 1987, he appeared as a guest star on Parpar Nechmad. He is also renowned for appearing in the comic series Zanzouri. He made further guest appearances on Polishuk and Bnot HaZahav.[5]