The 47-year-old former Portugal manager, who led his country from 2010 to 2014, became the team’s third coach in just two months after fellow countryman Marco Silva and Spaniard Sanchez.
"Olympiakos would like to announce the start of its co-operation with the Portuguese technician Paulo Bento," Olympiakos said in a statement.
Contract details were not disclosed but local media reported that Bento had signed a two-year deal.
Silva, who had guided Olympiakos to a record 43rd league title last season, resigned unexpectedly on June 23 and the 40-year-old was announced as his successor.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
However, poor pre-season form including defeat in the third qualifying round of the Champions League by Israeli debutants Hapoel Beer Sheva led to the dismissal of Sanchez after 48 days in charge.
Bento has also coached Sporting Lisbon, where he twice finished league runners-up and won two Portuguese Cups, as well as Brazilian team Cruzeiro.
(Reporting by Graham Wood, editing by Ed Osmond)
