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."