The 24-year-old striker, capped nine times for England, completed his permanent transfer to Upton Park from Liverpool in June after a successful loan spell last season.
Cole, who also played with Carroll at Anfield, believes the former Newcastle United forward has made vast improvements since making the switch from Liverpool, likening him to Didier Drogba.
"I've played with Andy at Liverpool and West Ham and the player who is playing for West Ham is full of confidence, strong, aggress and you can see what a great player he is," Cole told the club's official website.
"He had a difficult time at Liverpool, but the West Ham Andy Carroll is a real handful and a top player. He'll be looking at getting in the England squad and he can be anything he wants to be.
"You can look at a (Didier) Drogba, that's the level he can get to.
"He's a good lad and we're glad to have him here."
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