The Italy international has had promising spells at major European clubs blighted by behavioural problems both on and off the field.
|4/6||Liverpool are 4/6 woth William Hill to secure a top 4 finish in 2014/15|
"I believe we have the infrastructure, culture and environment to get the best out of him and help him achieve his true potential. We are a strong group here, committed to hard work and he will benefit from being around it," Rodgers told Liverpool's official website.
"I am looking forward to working with him and helping him learn more, improve and progress as a player. I'm sure the supporters will make him feel very welcome."
Liverpool have been trying to replace Luis Suarez this summer, after the Uruguayan left for Barcelona following his best ever season at the club.
But Rodgers is confident that in Balotelli, the club now have a player capable of producing yet more world-class displays.
"This transfer represents outstanding value for the club and I think we have done a really smart piece of business here," he said.
"There is no doubting Mario's ability; he is a world-class talent and someone who, for such a young age, has vast experience of playing at the very highest level.
"He has scored goals in the Barclays Premier League, in Italy, in the Champions League and for his country at international level.