Matt Le Tissier has urged Southampton boss Ronald Koeman to sign striking reinforcements before the transfer window closes.
The 31-year-old striker has signed a two-year deal with the Superleague champions and will play under Spanish coach Michel, who took over at the Athens club in January.
A statement on the club's official website also confirmed the Argentinian will wear the number nine jersey at the Karaiskakis Stadium.
Saviola left Malaga on June 30 when his one-year contract expired and he reportedly rejected an offer to return to his boyhood club River Plate, as well as shunning a move to Brazilian side Santos.
Olympiacos become the eighth club of Saviola's career, taking their place on a list that also features River Plate, Barcelona, Real Madrid, Sevilla, Monaco, Benfica and Malaga.
In 2001 he joined Barcelona from River Plate as a 19-year-old for £15million and, following loan spells at Sevilla and Monaco, he joined Real Madrid on a free transfer in 2007.
His stay at the Santiago Bernabeu was an unhappy one and in June 2009 he was sold to Benfica.
He experienced a return to form last season at Malaga, scoring eight goals in 19 Primera Division starts for Manuel Pellegrini's side, who reached the quarter finals of the Champions League.
And by joining the Greek champions Saviola will now get another chance to compete in Europe's elite competition.