The Giallorossi have beaten Premier League side Fulham to the player's signature, who joins the Italian capital club on a two-year deal for a fee of €400,000
Goal.com revealed on Tuesday that the Serie A side had beaten Fulham to the Greece international's signature, who had previously revealed he would not be renewing his contract with the Athens outfit.
The Giallorossi confirmed on their website on Wednesday that they had agreed a €400,000 deal for the 27-year-old, who has signed a contract until 2015, with the option to extend his stay by a further year.
Olympiakos had been keen to sell the versatile defender this month in order to risk losing him for nothing at the end of the season, and had allowed him to fly to Italy to complete a medical on Tuesday.
Torosidis is likely to watch his new side from the stands when they take on Inter in the Coppa Italia semi-final on Wednesday, but he could be available for selection for the Serie A clash with Bologna on Sunday.