The Turkish giants revealed the news on their website on Monday, stating that the 56-year-old will replace compatriot Roberto Mancini on a two-year deal.
Prandelli will arrive in Turkey on Monday evening before signing his contract and visiting the club's training base to meet the players on Tuesday.
Galatasaray had been in talks with Prandelli after the 56-year-old resigned from the Italy job when the Azzurri were eliminated from the competition, having failed to get out of their group.
Prandelli will replace Mancini at the Turk Telekom Arena following his departure from the post by mutual consent in June after just nine months in charge.
Mancini led the club to a second-place finish in their domestic league, and to the last 16 of the Champions League.
Galatasaray sporting director, Tomas Ujfalusi, recently admitted that Prandelli’s knowledge and experience within Italian football would be important in helping him build on the work that Mancini did while at the club.
“When Mancini did not want to continue, I wanted to bring in Cesare,” Ujfalusi was quoted as telling Gazetta dello Sport.
“In Florence he coached me and thanks to him I grew so much. At the World Cup he was unfortunate, but he had a great four years."
He added: “The Italian schooling can also help Turkish football. Roberto has worked so hard on tactics and did improve the team."