The Dutchman had stalled over accepting the Turkish champions' offer, but the club have now announced that his move to the Turk Telekom Arena will soon be confirmed
The Dutchman has been frozen out of Andrea Stramaccioni's side since September thanks to a dispute over pay, and the Istanbul giants confirmed that they were interested in signing him early in January.
A fee was swiftly agreed with the Nerazzurri over a transfer of the former Real Madrid man to the Turk Telekom Arena, but the player stalled over accepting their offer.
Goal.com exclusively revealed that Liverpool were also in the hunt for Sneijder, but the player has elected to continue his career in Turkey.
"The club have reached agreements with both Inter and Wesley Sneijder over a transfer," an official statement read.
"The conditions of the agreement will be announced when the player has passed medical checks. In addition, we will announce his time of arrival."
Sneijder, who will join the Turkish club once a medical has been completed, said that he is really looking forward to leaving San Siro to play under coach Fatih Terim, and hopes that he will be able to sign before their fixture on Sunday January 27 against Besiktas.
Speaking to Galatasaray.com, he said: "I'm very excited, I'm anticipating the day when I will wear the Galatasaray t-shirt. I know how much Turkish people are attached to football.
"I heard so many things about Fatih Terim. I know his career in Italy. It will be nice to work together.
"I feel great about the move [and] I want to play against Besiktas. I'm planning to learn Turkish as soon as possible."
Galatasaray are currently top of the Super Lig, two points clear of second-placed Besiktas.