The Inter midfielder was met by a welcoming committee when he landed at Ataturk Airport in Istanbul on his way to a medical assessment.
Galatasaray had a 10million-euro bid for the Holland star accepted two weeks ago, and a statement on Sunday read: "The transfer of Wesley Sneijder from Inter Milan has been agreed.
"The conditions of the deal will be made public and the player will sign the contract after health checks."
A short conversation between Inter president Massimo Moratti and Sneijder was released on the Serie A club's website on Sunday evening, in which both parties revealed the Dutch international was close to calling time on a successful spell at the San Siro.
Reports in Italy and Holland suggested Sneijder and his agent Soren Lerby met with Galatasaray director Lutfi Arigogan in a Milan hotel to finalise the details of a three-and-a-half year contract.
Sneijder 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.
This week saw Moratti urge Sneijder to make a "professional" decision over his future in Milan, where he won the treble under Jose Mourinho in 2010. The pair cleared the air before Sneijder headed for decisive talks with representatives of the Super Lig leaders.
Moratti told the club's website: "I met Sneijder. I wanted to have a chat with him, I thought we needed to.
"Have we made peace? I don't think there was ever a war in the first place, and certainly not with me personally.
"Did we chat to see if we were all moving in the same direction? Which one? It's a surprise...
"Is he close to a move to Galatasaray? Yes, I think so."
The playmaker, who joined Inter from Real Madrid for 15m euros in 2009, indicated he was ready to move on.
"I spoke a lot with president Moratti because we have a good relationship, we had a good talk, nothing more than that."