Copti was born in Jaffa to an Arab Christian family. His mother, Mary, is an educator and school principal of the Arab - Jaffa democracy school, and his father, Ilya, is a carpenter. Cobti received his BA from the Faculty of Mechanical Engineering at the Technion.
His first full-length feature film Ajami won the Ophir Award in Israel, the Camera d'Or Special Mention at the Cannes Film Festival. His film was also nominated for the 82nd Academy Awards in the Best Foreign Film category and has won more than 15 awards worldwide.
Formerly a mechanical engineer, he has also written, directed and edited several fiction, documentary and experimental short films. Copti was on the jury of the Tribeca film festival as well as at the Thessaloniki Film Festival in 2010 and president of the Human Rights Award in the Istanbul International Film Festival 2011. Copti was part of the team that launched the Doha Tribeca Film Festival and the Doha Film Institute (DFI) and he headed the DFI's education department until November 2011.