Levy was born in Jerusalem to immigrant parents who were of Kurdish Jewish origin from Cizre, Turkey.

He served as head of Jerusalem branch of the Israel Police between 2000 and 2004, winning the Knight of Good Government award in 2002.

Following Yesh Atid's coalition agreement with Likud, he was appointed to serve as Deputy Finance Minister.

In the build-up to the April 2019 elections Yesh Atid joined the Blue and White alliance, with Levy placed twenty-second on its list.

As part of the agreement between Naftali Bennett and Yair Lapid to form a "change" government, Levy was elected Speaker of the 24th Knesset on 13 June 2021, defeating Ya'akov Margi of Shas.