The Dutchman has been frozen out of Andrea Stramaccioni's side since September thanks to a dispute over pay, and the Istanbul giant confirmed that it was 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 the offer.
"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."
Galatasaray is currently top of the Super Lig, two points clear of second-placed Besiktas.