The appointment was announced by chairman Burak Elmas during a news conference.
Galatasaray previously parted ways with Terim by mutual consent following the team's poor results in the Turkish Super Lig.
Torrent, 59, was Spanish manager Pep Guardiola's assistant at Barcelona, Bayern Munich, and Manchester City between 2007 and 2018.
The Spaniard later managed Flamengo in Brazil and New York City as the Red Bulls head coach.
