Genoa sacked Davide Ballardini on Saturday with the club just one place above the relegation zone. They have won just one game from their 12 Serie A matches this season.
This will be Shevchenko’s first job in club management, having impressed as manager of his country in a five-year stint between 2016 and 2021.
The former Chelsea and AC Milan striker qualified Ukraine to the 2020 European Championship after missing out on a place at the 2018 FIFA World Cup in Russia.
Shevchenko guided Ukraine to the quarterfinals of EURO 2020 for the first time in their history before losing 4-0 to England.
"Genoa announces that Andriy Shevchenko has reached an agreement with 777 Partners and will lead the Grifone until June 30, 2024," Genoa said in a statement, before naming some of Shevchenko's achievements as a player and coach.
"Genoa and 777 Partners warmly welcome coach Shevchenko and wish him a fruitful time in charge of the oldest club in Italy."
"Kicking off this new adventure to bring back Genoa to its great history," Shevchenko wrote in a Twitter post.
Shevchenko’s first game in charge of Genoa will be against an AS Roma side managed by his former Chelsea boss Jose Mourinho after the international break.
Shevchenko won the much coveted Ballon d’or award in 2004 while on the books of AC Milan.
