After the player's agent Soren Lerby claimed on Friday that a deal could be done this weekend, the Turkish club admitted on Saturday that they were closing in on the Netherlands international.
Galatasaray have released a statement on their official website that a transfer had been agreed after discussions with Inter Milan.
The next step is to agree personal terms with the Dutch midfielder, who is still reportedly holding out for an alternative option.
The statement read as follows: "Galatasaray have agreed on the transfer of Wesley Sneijder with FC Internazionale.
"Discussions are ongoing with the player."