World Bulletin / News Desk
The signing ceremony took place in Galatasaray's club headquarters, where Terim and chairman Dursun Ozbek held a news conference.
Ozbek said Terim was the "only name that comes to mind, considering the situation that Galatasaray is in right now."
Galatasaray, which started the 2017/2018 season in good shape, lost their first-place spot a couple of weeks ago.
After last week's Yeni Malatyaspor Super Lig defeat, Croatian manager Igor Tudor was sacked by the management.
Ozbek said Terim is the man to take Galatasaray to the Super Lig title.
Terim also addressed the media, thanking Galatasaray fans and management for making the deal happen.
"I spent my life at Galatasaray. Sometimes there are break-ups, but allegiances are heavier than those break-ups," Terim said.
"After meeting with Mr. Ozbek, I thought I should shoulder the responsibility."
Terim said Sunday’s league match against Goztepe would be against one of the breakout teams of the season.
"We do not have to worry, but we have to be quick. We have lots to do. Hopefully we will be successful against Goztepe," he said.
Terim said his new team "does not have a left back with a left foot."
"The one we have [Iasmin Latovlevici] is currently injured. We have to find a solution when the transfer window opens."
The Istanbul club’s board announced Terim as the new manager late on Thursday.
Galatasaray’s official Twitter account shared a post reading: "And just where we left off... HE IS BACK! #FatihTerim."
The 64-year-old manager had been linked earlier this month with a possible move to Bosnia to head the country’s national side.
This will be Terim's fourth spell with Galatasaray; he first managed the team in the 1996/1997 season, where he achieved major success, domestic and European.
He left the club for Fiorentina and Milan after the 1999/2000 season, but rejoined the club in 2003/2004.
Terim's previous tenure with the club started in the 2011/2012 season; he managed to take the team to the quarter-finals of the UEFA Champions League in 2012/2013.