Bellamy joined Liverpool on a two-year deal on Wednesday after leaving Manchester City, where he found himself frozen out under manager Roberto Mancini.
The transfer means that the Welshman has another chance to make an impression at Anfield, four years after leaving the club following a season that featured nine goals and a controversial bust-up with John Arne Riise.
"It's a great signing. As a kid he always said he was a Liverpool fan," said Carragher to liverpoolfc.tv. "I think he was quite disappointed with how it finished, with how he left. He'd have liked to have done a lot better and hopefully this gives him the chance to do that.
"For the last few years at Man City he has been excellent, not just as a striker but as a wide player. In the squad we've probably only got Stewart Downing as an out-and-out wide player. I think Craig prefers to play as a striker but he could certainly do that job for us."
Carragher was also pleased to see the defence reinforced with the arrival of 6' 6" Uruguay centre-back Sebastian Coates, who impressed during this summer's Copa America.
"I haven't seen a lot of him but I think he got young player of the tournament," the veteran centre-back said. "That shows he's got great quality and I think it's going to be a great addition to the squad. You can't think of yourself, you have to think of the club.
"One centre-back (Sotirios Krygiakos) went so we needed another. Time will tell how good the lad is but his pedigree looks fantastic. He's probably been brought up playing a different type of football than I have, a South American style - so maybe I can learn from him as well.
"It's not always about the older players helping the younger - it can work vice-versa. You're always learning from different people."