Carroll completed a permanent move to Upton Park earlier in the summer after scoring seven goals in 22 games while on loan from Liverpool last season.
And Cole, who spent time with the England striker while at Liverpool, is convinced that the 24-year old will become a key signing for the Hammers.
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"It is a boost for the club and shows where we are going,” he told the club's official website.
“Andy Carroll is a young, England centre-forward and clubs do not usually sell them. He's a big talent.
“He did a good job and we just want him to get fit and come back because he is a big part of our team."
Cole also revealed he is also anticipating a big season for himself and is refusing to rule a possible England call-up for next year’s World Cup.
“Every year is a big year in football, you always have your goals but I'm just enjoying myself," he added.
"I have played over 50 times for my country so if I can get playing you never know but at the moment I'm just concentrating on West Ham."
This season Cole hopes to realise his dream of taking the Hammers to Wembley, because the club has been "starved of success".
"I think the ambition of the club at the moment is improvement," he said.
"But for me personally, I would love to finish better than 10th, but equally I'd love to take this club to Wembley.
"Because at the end of the day, they are the days you remember in your career - it would be a massive achievement."