Hasi, 45, signed a two-year-contract with the Super League club after several days of talks, and he replaces previous boss Takis Lemonis.
Olympiakos won their 44 league title -- and their 17th in the last 19 seasons -- in May but experienced a turbulent campaign, making three coaching changes and losing out in the Greek Cup semi-finals to AEK Athens.
"I am very happy to join this great club; I faced the club twice while with Anderlecht and it was then I realised the scale of the club's grandeur and the special atmosphere of the stadium - it made some players actually afraid," Hasi told reporters.
"I come here with great ambitions, the first of which is to qualify for the Champions League group stage," he added.
Hasi took charge of Anderlecht in 2014 after being an assistant coach at the Belgian club for six seasons.
Last season he joined Legia Warsaw and led them into the Champions League group stages via the qualifying process, but was sacked in September due to poor results in the league.
Owned by Vangelis Marinakis, Olympiakos will be looking for more stability under Hasi.
Portuguese coach Paulo Bento had started out the 2016/17 season as Olympiakos coach, but he was sacked after a poor run of results in March.
Interim coach Vasilis Vouzas took the helm for several matches but then Lemonis was quickly brought in for his third spell in charge to see out the season.
Hasi's first task will be to negotiate two rounds of qualifying for European football's elite competition; the third qualifying round in late July, followed by the playoffs.
(Editing by Keith Weir)
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