Cole, who has led the Hammers’ scoring charts for the last four seasons, is relishing the prospect of battling with Carroll for a starting berth.
“Every year, you have to have people challenging for places because it is healthy for the club,” Cole told the club’s official website.
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"I'm a guy who believes in that and you could get complacent if you know you are going to play week-in, week-out.
"It's better to always be on your toes and I welcome a challenge like Andy Carroll because he is one of the best target men around in the Premier League and it's just going to reinvigorate me to be a better player."
As well as praising strike rival Carroll, Cole also spoke of his admiration for new arrival Yossi Benayoun, who played with Cole at West Ham during the 2006-07 season.
"Yossi is a brilliant character and a great player as well - we all know that,” Cole continued. “He has finally come home and he's back where I believe he belongs.”