Cottee is of the belief that Carroll is a perfect fit for the Hammers and Sam Allardyce and he knows the fans will continue to get behind him from the off.
He told whufc.com: "For the way Big Sam wants to set his teams up, I think Andy slots right in for him. Playing in the system with Kevin Nolan pushing on from midfield, they have a telepathic understanding and they got on really well on and off the field.
"With Kevin pushing forward you need a big target man, you need someone who is going to hold the ball up, bring the others into play and then if you get the likes of Matt Jarvis supplying the crosses, he's always going to be a danger.
"Whatever club you go to, it's great to get that adulation from the fans, when they respect you as a player and understand what you bring to the table.
"Andy will get that, and I think from his point of view there's a World Cup at the end of next season, and if you're not playing football you won't be in Roy Hodgson's plans.
"So personally I think it's a great decision from Andy - coming here and playing his football in front of such passionate support will be great for Andy, and if he can get into the World Cup squad then it's great for the Club too because it means Andy's playing well and the team's doing well."