Galatasaray said in a statement on its website Monday that Mancini signed a three-year contract and will be paid 3.5 million euros for the upcoming season, with his salary upped to 4.5 million euros for the next two campaigns.
Terim's contract was terminated by the club last week after he rejected a two-year extension.
One of Turkey's best known coaches, Terim last month started his third stint as manager of Turkey's national team.
Galatasaray plays Juventus on Wednesday in the Champions League.
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