The 24-year-old signed a six-year deal at the Boleyn Ground following a season-long loan stint from Liverpool.
The Hammers are due to move into the ground, which was made famous during the London 2012 Games, in 2016.
"It's massive," Carroll told West Ham TV. "The club's only going one way and that's what I want to be a part of. The fans are never quiet [at the Boleyn Ground] and it's going to be even better at the Olympic Stadium when more people can fit in. I can't wait."
The striker is said to be on wages of £100,000 a week.