After reportedly falling out of favour with Inter due to contract renewal issues, Sneijder agreed a three-and-a-half-year deal with Turkish giants Galatasaray on 20 January 2013 for a fee of €7.5 million. Thousands of Galatasaray fans welcomed the Dutch international at the Istanbul Atatürk Airport as soon as Sneijder's exact arrival time was announced by the club on their official website. Sneijder signed the official contract on 21 January at the Türk Telekom Arena, home of Galatasaray. During the press conference, regarding the questions about Gala legend Gheorghe Hagi, Sneijder said, "He was a legend, and I want to become a legend." Later, he appeared on the club's official TV station Galatasaray TV, where he answered several questions about his transfer to Galatasaray and personal life. He also sent out a message addressing the Galatasaray fans: "Thank you for the support. I'm really proud, and I will make you guys even more proud. I'm happy to be here, and I can't wait to play my first game for you guys."
On 27 January, Sneijder made his debut, coming on as a substitute in a 2–1 win against rivals Beşiktaş. Sneijder received a warm reception when he replaced Umut Bulut. He scored his first goal on 25 February in a 4–2 home win against Orduspor, where he produced a finesse shot from the edge of the box, turning the game back on for the home side as Galatasaray were down by two goals. On 9 April 2013, Sneijder scored Galatasaray's second goal in a 3–2 win over his former club Real Madrid in the quarter-final stage of the Champions League. On 5 May 2013, Galatasaray beat Sivasspor 2–1 to win the 2012–13 Süper Lig, this gave Sneijder a league title in a fourth different country.
After using the number 14 shirt in his debut season with Galatasaray, Sneijder was given the number 10 shirt previously worn by Felipe Melo for the 2013–14 Süper Lig season following a squad number reshuffle. On 1 December 2013, when Galatasaray drew with Kasımpaşa Spor Kulübü, Galatasaray manager Roberto Mancini, in response to the question "where is Sneijder?" asked by reporters during a post-match interview answered, "Sneijder has left and I do not know where he has gone," while Galatasaray's official website had earlier informed the media on the reason for Sneijder's absence.
On 11 December 2013, Sneijder scored a late winning goal against Juventus in a 1–0 UEFA Champions League win to qualify Galatasaray for the knockout phase. On 2 February 2014, Sneijder scored a hat-trick in Süper Lig encounter against Bursaspor in a 6–0 win.