Carroll, 24, was signed for an undisclosed club-record fee by the Hammers yesterday after impressing for large spells of a season-long loan deal at the club last season.
The former Newcastle forward was identified by Allardyce at the start of the summer as his main priority ahead of a second successive Barclays Premier League campaign.
With Carroll's close friend Kevin Nolan captaining West Ham, and relationships struck up during his spell in east London, Allardyce believes the experience of the loan move was invaluable in enticing Carroll to the club.
"Our relationship over the 12 months he was here was key to this deal," he told the club's official website.
"He came to us in a difficult frame of mind and had suffered with injuries but the support the coaching staff and the rest of the boys that work so hard behind the scenes was something he felt very comfortable with in the end.
"He met new team-mates over the year and enjoyed their company and I think that definitely helped him to make the decision to return to West Ham. So not only did the loan pay off by us finishing 10th in our first season back in the Premier League but it has paid off by him choosing us."