The 22-year-old completed a shock club-record £35million transfer from Newcastle after Fernando Torres was sold to Chelsea for £50million.
Carroll has inherited the Spain international's number nine shirt, worn by other Liverpool greats like Ian Rush and Robbie Fowler, and he believes he is equipped to follow in their illustrious footsteps.
"Goals have always been in my game so I'm very confident I can score for Liverpool," he said. "It's a great feeling. The number nine is a big number and the one I wanted. To get it at Liverpool is a great feeling.
"I want to go out there and play the football that has brought me here. I'll bring as much as I can to the team - I'll score goals, create chances, hold up the ball and just try my best really.
"They have spent a lot of money on getting me here and I just want to repay them for what they have spent. I'll do my best and think I can do it. I want to win trophies with this club and help push us forward."
Source: PA