The 28-year-old was expected to leave Internazionale this month after failing to agree a new deal with the 2010 Champions League winners, who wanted the playmaker to take a pay cut.
Galatasaray have been in pole position to sign Sneijder for much of the January transfer window after agreeing a £6.2m deal with Inter, and the midfielder is close to completing the switch.
On Sunday, the Super Lig club released a statement which said: “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.”
Inter chief executive Massimo Morratti also confirmed Sneijder was on the brink of leaving the San Siro after the pair met last week.
“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.”
Sneijder scored 22 goals in 116 appearances for Inter, winning the Serie A title, Coppa Italia and Champions League crown in 2010.