The club announced the deal to fans on Sunday afternoon and confirmed that the Ukrainian coach will take charge until June 2024 and will be tasked with keeping the Grifone in Serie A after a disappointing start to the season.
They sit 18th in the table having won just one of their opening 12 fixtures. They have drawn six and lost the other five.
Shevchenko was in charge of Ukraine at Euro 2020 and they reached the quarter-finals where they were beaten 4-0 by England.
He won the Ballon d’Or as a player in 2004 and the Champions League in 2003/04 with Milan.
Genoa’s statement said: “Genoa CFC and 777 Partners warmly welcome Mr Shevchenko and wish him success at the helm of the oldest club in Italy.”
