The striker completed his move from AS Roma yesterday.
Rodgers told liverpoolfc.com: "Yes, I've known him since he had just turned 16 years of age. We (Chelsea) took him in from Bologna when he was 16 and he progressed incredibly well as a young player to go on to play for the first team at Chelsea.
"It didn't work out in terms of he couldn't agree a contract, but before he left I took him on loan to Swansea and he made a big, big impression there and really helped us in our promotion charge that season.
"He left and went away (to Roma) and in the last season he's done incredibly well.
"I think the supporters will love him. As I said, he's a goalscorer, but he's a multifunctional player who can play in a number of positions - and someone I believe has got great growth.
"He's one of the few young players in the full Italian squad. I'd anticipate that over the next two or three years he'll really progress and I'm sure do very well for Liverpool."