Muslera saw new contract talks with Lazio collapse last week.
It's understood that Muslera, who was on 1.4m a campaign in Rome, will sign a contract until 2016 worth 2.5m a year - with bonuses that could earn him an extra 300,000.
"I've received offers from Spain, but I have chosen Galatasaray," the Uruguayan custodian confirmed.
"They were the most insistent club that wanted me. I'm going to Turkey to be successful."