De Zerbi, 43, started his managerial career in the Italian lower leagues before he caught the eye of Serie A side Sassuolo, guiding them to eighth place in the 2020-21 season. He was head coach of Ukraine's Shakhtar Donetsk last season.
"I am absolutely thrilled Roberto has agreed to become our new head coach. Roberto's teams play an exciting and courageous brand of football, and I am confident his style and tactical approach will suit our existing squad superbly," Brighton chairman Tony Bloom said.
De Zerbi takes over from Potter, who left for Chelsea earlier this month after three highly successful seasons in charge.
Brighton, who are fourth in the Premier League with 13 points from six games, next travel to Liverpool on Oct. 1 following the international break.