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Benteke becomes the Reds' second most expensive signing, on what the club describe as a "long-term contract".
Liverpool, who last week sold forward Raheem Sterling to Manchester City for £49m, triggered a release clause in Benteke's contract to make the 24-year-old their seventh summer signing.
Belgium international Benteke scored 49 goals in 101 games for Villa after signing from Genk for £7m in 2012.
He told the Liverpool website: "I'm very happy to be here. I came here to win trophies. I came here to reach some great goals with the team.
"It was the right club for me because I had a good chat with the manager and I wanted to be part of his project."
Liverpool struggled for goals last season following the £75m sale of Luis Suarez to Barcelona and prolonged injury absences for England international Daniel Sturridge as they finished sixth in the Premier League.
Signings Mario Balotelli and Rickie Lambert produced three league goals and, after acknowledging the lack of scoring last season, manager Brendan Rodgers has added Benteke to revive the Reds' attack.
Liverpool have also signed forwards Danny Ings from Burnley and Brazil international Roberto Firmino from Hoffenheim, while Benteke's international team-mate Divock Origi has returned to the club after spending last season on loan at Lille.
Benteke missed the 2014 World Cup in Brazil with an Achilles tendon injury but returned to action last October and scored 15 times to help Villa stay in the Premier League and reach the FA Cup final.
Former Villa manager Paul Lambert, who brought Benteke into English football, believes he will do well at Anfield.
Lambert told BBC Sport: "He's a brilliant number nine. He won't need just crosses to come into the box. If he gets the service he'll get goals.
"That's the type of guy he is and on his game he's a handful. I'm delighted for him. He's earned that move and if he can do what I think he can do, he'll do great for them.
"He's going to have to handle the expectancy level of winning [at Liverpool]. When you speak to Christian, he has a great belief in himself to do well."
Former Liverpool striker John Aldridge is also excited to see Benteke lead the Liverpool forward line, telling BBC Radio 5 live: "He gives something different, a massive presence up front.
"It's a fallacy when people say he doesn't play the Liverpool way. He knocked Liverpool out of the semi-final of the FA Cup when he played through the middle.
"He's very quick, very strong, very aggressive and that's something we haven't had for some time up front. It's something I'm really happy with and I think he'll bring a lot to the squad.
"I'm a lot more optimistic than I was this time last year. The strikers only scored eight goals last year, we can only do better than that going forward."
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Liverpool have signed Aston Villa striker Christian Benteke for £32.5m.