Benteke scored in Aston Villa’s 2-1 victory over Liverpool in the semi-finals of the FA Cup at Wembley in April.
The Belgium international had been a regular scorer for Villa since moving to the Premier League in the summer of 2012 from Genk.
In his first season, he scored 23 goals in all competitions and, following an injury-hit second campaign, added another 15 in 2014/15.
And Rodgers expects great things from Benteke, telling Liverpool’s official website: “For me, I think he’ll prove to be a bargain for the club. I really do.
“I’ve read and seen things about his game but in the short period of time he’s been in, I’ve been even more impressed.
“I’ve seen him up close now for three years, stood at the side of the field and watching this guy – not just his power and strength but also his footballing ability.
“One of the goals I remember he scored against us at Anfield, he ran half-way through the field. This isn’t someone who lacks pace, movement and intelligence.
“He’s not just a guy who you chuck the ball up to. Of course, his strength allows you to keep the ball, but he’ll really help the unpredictability of our game this season.
“We know he can play football, we know he can play counter-attack, but we also know when we cross the ball, we’ve got a real presence in the box that is going to allow us to keep the ball in the box for periods of time and for others to get goals from.
“Obviously he doesn’t set the price and I’m thankful the club have brought him in because I really think at 24 years of age, he’s going to be a huge asset for us.
“He’s surprised people in the early stages of life at Liverpool with that mobility and the quickness of his feet – and his natural power and strength is there to see.”