Italy striker Mario Balotelli has completed his £16m move to Liverpool from Serie A side AC Milan.
The former Manchester City player, 24, agreed a long-term deal with the Merseyside outfit but did not feature as Liverpool lost 3-1 to his old club on Monday night.
Balotelli left City 17 months ago after scoring 30 goals in three seasons.
"I think we have done a really smart piece of business here," said Reds boss Brendan Rodgers.
"This transfer represents outstanding value for the club."
Balotelli, who will wear the number 45 shirt, said he had made an error leaving England in January 2013.
"I'm happy to be back because I left England and it was a mistake," he said. "I wanted to go to Italy, but I realised it was a mistake."
The former Inter Milan player added: "English football is generally better. English football is beautiful."
Balotelli will watch Liverpool's game at City from the directors' box after meeting up with his new team-mates in the changing rooms before the match. After the game, he will travel back to Liverpool on the team coach.
"There is no doubting Mario's ability," added Rodgers. "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."
Liverpool are understood to have sought assurances from Balotelli, who has scored 13 goals in 33 appearances for his country, about his commitment and off-field behaviour.
He is a controversial figure, who has fallen out with previous managers and got into scrapes off the pitch.
But Rodgers insisted before the deal was done that any player he signs will not be a disruptive influence.
"I'm happy to be here," said Balotelli. "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."
|The life of Mario|
|Balotelli joins Manchester City in August 2010 for £24m from Inter Milan. He scores 30 goals in 80 games and helps the club win their first Premier League title.||He struggles with discipline at City and is involved in a training-ground altercation with then-manager Roberto Mancini, prompting his departure from the club.|
|AC Milan sign Balotelli from City in January 2013 for £19m and the former Inter Milan striker goes on to score 30 goals in 54 games.||Having impressed for Italy in Euro 2012, scoring two in the semi-finals, he nets the winner in a World Cup group win over England in Brazil.|
There had been suggestions former Chelsea forward Samuel Eto'o was on standby to sign for Liverpool had the Balotelli deal broken down.
The Italian becomes Liverpool's ninth signing of the summer transfer window and takes their spending to more than £100m.
The Reds recouped £75m from the sale of last season's top-scorer Luis Suarez to Barcelona.
Balotelli was a big hit with City supporters, helping the club win a first league title since 1968.
But he was also in the headlines for several off-the-pitch incidents, including a training-ground row with then-manager Roberto Mancini.
In his second season in Manchester, he scored only three goals in 20 games.
The striker agreed a four-and-a-half-year deal with Milan in January 2013 and played for Italy at the World Cup in Brazil.
Former Liverpool defender Gary Gillespie believes the signing of Balotelli is a big risk for his former side.
"His reputation does go before him," he told BBC Radio 5 live.
"Brendan Rodgers, out of all the young managers, would probably be the one to handle him better than most, but I still think it's a big gamble."
But Mark Lawrenson, another former Liverpool defender, disagreed.
"For £16m, it's not too much money," he told Radio 5 live. "When you think that Shane Long went to Hull for £12m and Ross McCormack to Leeds for £11m, it's not a lot of money in comparison.
"He's made lots of mistakes in the past - and he might make some more - but what's the worst that can happen? If it doesn't work, someone else will take him in the future, either in January or next summer.
"People say he might upset the dressing room, but everywhere he has played all the players have loved him and he's become a popular guy."