The Holland international, 28, had been at odds with the Serie A club since he refused to take a pay-cut in September and has ended a long-running saga by moving to Turkey.
Inter accepted a Galatasaray offer of 10m euros last week, and a statement on galatasaray.org 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."
Despite Inter president Massimo Moratti revealing the playmaker was nearing the San Siro exit door, Sneijder appeared to suggest a reconciliation with the Nerazzurri was still possible.
But the player confirmed the Galatasaray deal in an interview on Sunday night, saying: "I'm so excited right now. A worldwide club Galatasaray. I cannot wait for the first game (v Besiktas).
"I've heard so much about, and I know Fatih Terim. Together will be great to work with."
Several Premier League clubs - including Liverpool and Tottenham - had previously been linked with making a January transfer swoop for Sneijder.