Allardyce expects big things from their England man.
"Andy's disappointment at not being given a chance at Liverpool was something he had to overcome," he told talkSPORT.
"But I think he's done that now and he's realised he needs to look at his future at not his past.
"Andy decided to stay where he felt very comfortable.
"He's got more accustomed to life in London, more accustomed to the club and made some very good friends in the squad.
"He's only 24-years-old, so he's still got a long way to go to reach his best, and hopefully we'll be the club to deliver a better player and a better Andy Carroll in the next few years.
"The fans love Andy, they love to see players committed to the shirt, they want to see passionate players. "It'll be great for him, for England and certainly for West Ham."