The Greek champions, who sit a point behind PAOK in this season's Super League, parted company with Michel on Tuesday.
Pereira has now been installed as the Spaniard's successor, with his first match at the helm set to come at Xanthi on Sunday.
A brief statement on Olympiacos' official website read: "Olympiacos FC announce the beginning of their collaboration with Portuguese manager Vitor Pereira."
Pereira, previously linked with Everton, was the assistant manager to Andre Villas-Boas at Porto, and went on to lead the club to successive Primeira Liga titles after taking the top job in 2011.
He subsequently coached Saudi Arabian outfit Al-Ahli, but will now resume his career in Europe.
Olympiacos, who face Dnipro in the last 32 of the UEFA Europa League next month, will present their new coach at a press conference on Thursday.
