The former AC Milan star believes the striker made the right decision to move on and hopes he can redeem himself at Anfield after completing a £16 million deal
Balotelli made a fine start to life at Milan after joining them from Manchester City in January 2013, but failed to replicate that form in 2013-14 and was sold to Liverpool this summer for £16 million.
"If Balotelli wasn't happy at Milan and the club were not satisfied either, it was the right decision to part ways," Shevchenko told La Gazzetta dello Sport.
"But I saw Mario in action at the European Championship in Ukraine and Poland two years ago and he was a fantastic player. I refuse to believe that's all gone all of a sudden.
"Mario deserves another chance and Liverpool are giving him that chance. Liverpool are a great team and could have the ambition to win the Champions League.
"It's now up to Balotelli to overcome his difficulties and take his fate back in his own hands again."
The 24-year-old impressed on his Liverpool debut in the 3-0 away win over Tottenham at the weekend, but failed to find the net.