The Istanbul club last week revealed that they were in talks with the former Italy coach, who resigned after his country's disappointing FIFA World Cup campaign.
Galatasaray issued a statement on their website on Monday confirming that the 56-year-old will replace compatriot Roberto Mancini, who left the club by mutual consent last month.
He signed a new two-year deal to stay on as Italy coach in May, but stepped down after the four-time world champions failed to progress from Group D in Brazil - winning only one game against England.
Galatasaray announced last month that president Unal Aysal had held informal talks with former Manchester United manager David Moyes, but a spokesman added that Germany coach Joachim Low and United States boss Jurgen Klinsmann were the club's prinicipal targets.
