The former Italy international has left San Siro on a free transfer, and is expected to sign a contract with the Istanbul side in the upcoming days
Head coach Fatih Terim is desperate to add some more experience to his squad ahead of the 2012-13 campaign, and the former Milan trainer sees the 34-year-old Gattuso as the ideal addition to his midfield.
Gattuso is available on a free transfer after leaving San Siro this summer, and has previously been linked with a return to Rangers.
However, he is now set to join the Istanbul club instead after a move to the Scottish powerhouse fell through due to the ongoing financial problems at Ibrox.
Galatasaray have reportedly reached an agreement with Gattuso for a one-year deal worth €1.5 million, and the holding midfielder is expected to travel to Turkey shortly to complete the move.