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.
'People will remember us because we got to No.1 in the world rankings and achieved great things - but our biggest regret is that we didn’t win anything': Ex-Everton star Kevin Mirallas opens up on 'honour' of being part of nation's golden generation
‘I’m sure we’d have finished in the top four or five if he hadn’t joined Chelsea in January. Him leaving damaged the team, but we couldn’t stand in his way’: Alan Curbishley reflects on failed Champions League dream after selling key player
