The striker is reportedly a target for for Besiktas, but has stated that he will not be leaving the club, and that the 23-year-old's arrival is good for competition in the squad
The England international, who has joined the Hammers on loan from Liverpool adds to competition for places up front at Upton Park, but Cole, who has been linked to a move to Turkish side Besiktas, is not phased.
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"Andy Carroll is a good addition to the squad and hopefully he makes a positive impact to our side. Onwards and upwards.
"Competition for places is good for players and the team, you need it in every position. I feel it's gonna be a good season for the Hammers."
Hammers boss Sam Allardyce is also confident that Carroll can make an impact, with the Londoners having an option to buy the 23-year-old for £17 million if the team stay up this season.
"He was pleased to choose us with a number of other Premier League clubs interested," Allardyce told Sky Sports News.
"We've got a top-quality player and I'm delighted to have pulled it off. I first tried to sign him a long time ago and it did not look like it was going to happen, so I'm glad it has.
"He's a huge player in this division who scores goals and contributes to build-up play, and has many different aspects to his game which can help us be a force in this league.
"In your first year in the Premier League it's all about who's going to score the goals and who's going to take your chances, and I think in Andy we've added a huge amount of goals to the team.
"Hopefully we can give him the service and he can prove what a good goalscorer he is."