Terim, 64, has had three spells in charge of both Galatasaray and the national team. He left his job as Turkey coach in July after being involved in a brawl in a west coast resort town.
"Welcome to your home, emperor Fatih Terim," the club said on its official Twitter feed, using the nickname by which he is known in Turkey.
Terim signed a one-and-a-half year contract worth 3 million euros (£2.65 million), with a 500,000 euro bonus if Galatasaray win the championship, the club said.
"We are here to unite with our fans and create new success stories," he said during the signing ceremony at the club's stadium.
Shares in Galatasaray rose 5 percent on Friday after the club announced overnight that it had started talks with Terim. He has won six league titles with the club.
Galatasaray, which also won the UEFA Cup in 2000, lie third in the Turkish championship after suffering their fourth defeat of the season last weekend.
Terim's first assignment should be Sunday's league match against Goztepe.
Terim, also a former coach of Fiorentina and AC Milan, was previously in charge of Galatasaray between 1996-2000, 2002-2004 and 2011-2013. In his second stint with Turkey he led them to the Euro 2008 semi-finals.
Previous coach Tudor, who moved to Galatasaray from Karabukspor halfway through last season, had been widely criticised after the team allowed an eight-point lead in the standings to slip away.
(Writing by Daren Butler and Ece Toksabay; Editing by Paul Tait and John Stonestreet)
