The Giallorossi have beaten Premier League side Fulham to the player's signature. He joins the Italian capital club on a two-year deal for a fee of 400,000 euros.
The Giallorossi confirmed on their website on Wednesday that they had agreed a 400,000 euro 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 allowed him to fly to Italy to complete a medical on Tuesday.
Torosidis is likely to watch his new side from the stands when it takes on Inter in the Coppa Italia semifinal on Wednesday, but he could be available for selection for the Serie A clash with Bologna on Sunday.