Torosidis, 27, is set to sign a five-year deal that will see him pocket 2.5 million euros a year.
"Olympiacos can announce that an agreement has been reached with AS Roma for the transfer of Vasilis Torosidi," said a statement on the Greek club's website.
Fulham were also linked with a move for Torosidis, who joined Olympiacos from Xanthi in 2007.
He has been capped 54 times for his country.
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