The Holland midfielder, who has agreed a move from Inter Milan to the Turkish giants for 10 million euros (£8.4million), received a hero's welcome after flying into the capital's Ataturk Airport with his family.
Gala confirmed the 28-year-old met with head coach Fatih Terim as well as club board members on a tour of the facilities.
Terim said on Gala's official Twitter feed: "We have completed the transfer of a very important player. Sneijder is very happy here. He will start to prepare from tomorrow."
Sneijder added: "I feel I can be a success, I'm hungry for it. The welcome was incredible and it made me really happy."
He also Tweeted on his own account: ""I want to thank all the fans for this warm welcome."
Gala confirmed tonight that the former Champions League winner would undergo a medical on Tuesday morning. Provided no issues arise during his check-up Sneijder will put pen to paper on a reported three-and-a-half-year deal with the Turkish Super Lig leaders .
Sneijder's move ends a three-and-a-half-year spell at Inter during which he won a famous Champions League, Serie A and Coppa Italia treble in 2010 under Jose Mourinho.
And Inter president Massimo Moratti thanked Sneijder for making history at the Serie A club.
Moratti and Sneijder were at odds over the player's refusal to agree to a pay cut in the autumn, but the Inter chief paid a heartfelt tribute to the playmaker on Monday.
He told inter.it: "It's not just a case of affection but of gratitude, he will always be one of the most important figures in Inter's history and we were proud to have him with us, as Galatasaray will be.
"Everything was done correctly on Galatasaray's end. Their president and vice-president are very nice people.
"I think the player's happy too, otherwise he wouldn't have gone. The important thing is that it had to happen, and it has happened, so that's enough for me."
Sneijder, who joined Inter from Real Madrid for 15million euros in 2009, has not featured for the Nerazzurri since a 2-0 victory at Chievo in September after publicly refusing to take a two million euro pay cut on a contract that ran until June 2015.
Head coach Andrea Stramaccioni maintained the playmaker's absence from the first team was solely a tactical decision, despite Inter's clear difficulty in keeping pace with league leaders Juventus through an injury crisis.
Meanwhile, Moratti claimed he would not rush into making a formal approach for Corinthians midfielder Paulinho, despite the departure of Sneijder.
Inter are reported to be lining up Corinthians midfielder Paulinho as a replacement, but Moratti urged patience.
"One thing at a time," he told inter.it. "We've just finished (the Sneijder deal), then we'll see what else we need to do.
"I don't know, it depends if it's worth it. Everything costs a lot in Italy so I don't really think anything will be done.
"A player of his type, with his characteristics, will always be useful. But it's a matter of cost."
Atalanta winger Ezequiel Schelotto is also a reported transfer target for Inter, who currently trail Serie A leaders Juventus by nine points.