The 48-year-old Blessin signed a contract until 2024 after Genoa, currently struggling in Italy’s top tier, paid his release clause from Belgian soccer club Oostende.
Blessin also previously coached the youth teams at Leipzig.
Shevchenko had also signed a contract until June 2024 when he took over two months ago.
But the former AC Milan and Chelsea forward was fired on Saturday after winning just one of his 11 matches in charge.
Under-17 coach Abdoulay Konko was in charge of Genoa on Monday for the 6-0 loss at Fiorentina.
The club, which was bought by American private investment firm 777 Partners in September, is in penultimate place in the Serie A standings, six points from safety.
The Colorado Rapids continued a flurry of contract extensions Wednesday, announcing that midfielder and captain Jack Price has re-upped through the 2024 MLS season with club options for 2025 and 2026.
Price, 29, is renowned for his set-piece service and has provided a league-leading 22 assists off dead balls since 2019.
“Jack has become the heartbeat of our team and one of the best midfielders in the league since his arrival four years ago,” EVP & general manager said in a release. “His leadership, selflessness and elite set-piece deliveries have been a vital part of our on-field success and we’re thrilled to secure his future in Burgundy.”