Balotelli, who was photographed practising on a pitch at Melwood wearing a Liverpool training top, is expected to cost £16million.
Balotelli, who will wear his favoured No 45 shirt, is understood to have the option of a fourth year.
The striker won the Champions League with Inter Milan in 2010 and has ambitions of repeating the feat with Liverpool on the Reds' return to Europe's elite competition.
He told Liverpool's official website: "I always start a competition wanting to win it. We will see. I want to win another Champions League for sure, because the Champions League wasn't all mine, I was in a team. I want to take this team to the Champions League."
Balotelli also admitted that just 18 months back in Milan had convinced him he should return to the Premier League.
"English football is generally better. English football is beautiful."
Balotelli was given a rough ride by Liverpool fans during his visits to Anfield while with City, but he has already been given a warm welcome by supporters who had been mourning the departure of Luis Suarez.
He added: "I didn't expect it [the warm reception] because whenever I played against Liverpool, the fans weren't nice with me but that's normal - it's football! Now that I play for Liverpool, I can see the expectation in people. They're very happy and that makes me very happy at the same time.
"To play here for Liverpool excites me, but if you're an opponent it's difficult.
"Liverpool are one of the best teams here in England. The football is very good here. It's a great team with young players, and that's why I came here."
"I'm very happy. We've been talking about coming here and now I'm happy to be here," said the Italy forward. "Liverpool are one of the best teams here in England and the football is very good here.
"It's a great team with young players, and that's why I came here."
Balotelli is Liverpool's ninth signing of the close season. He will travel to the Etihad Stadium to watch Brendan Rogders's team meet his old club Manchester City in the Premier League on Monday night.
He departs Milan after 18 months where he scored 30 goals in 54 matches.
Balotelli scored against England in a 2-1 win in their World Cup match in Manaus. He won the Premier League title with City in 2012, and the FA Cup a year earlier.
He claimed the Champions League and three Serie A titles with Inter Milan, and has netted 13 times in 33 outings for his country.
However, his eccentric personality has led to clashes with coaches Jose Mourinho and Roberto Mancini, and supporters, most notably those of Inter and Juventus.
But Reds boss Brendan Rodgers feels he can get the best out of Balotelli, who replaces controversial striker Luis Suarez after the Uruguayan joined Barcelona for between £65m and £75m - just under five times the amount Liverpool spent on the Italian.
"This transfer represents outstanding value for the club and I think we have done a really smart piece of business here," Rodgers told Liverpool's official website. "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. 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. 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."
Balotelli will be at the Etihad Stadium on Monday night to watch Liverpool's match against his former side Manchester City.
The Italian will travel with five of his new team-mates who have not been included in the match-day squad and will meet those who are scheduled to play in the dressing room before kick-off.
He will then watch the game from the directors' box before travelling back to Liverpool with the rest of the squad on the team coach.
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