Allardyce described signing Carroll as his number one priority at the start of the close season, so was naturally pleased to complete the deal.
"After a long chase I am delighted that we have finally secured our very important acquisition in terms of ability and age," Big Sam told whufc.com.
"We expect him to enhance his reputation even further with West Ham and become one of the major strikers in the country and become an England regular - we hope he will produce for West Ham and England as we prepare to move into the Olympic Stadium in 2016.
"We've acquired a player who was recently the most expensive British player in the history of football. We haven't done it cheaply, but we have definitely done it wisely."
Allardyce believes the long-term nature of the contract penned by Carroll shows the belief the striker has in the Hammers' potential to keep on growing.
He continued: "The size of the contract is a statement of West Ham's belief in Andy and Andy's belief in West Ham. Our relationship over the 12 months he was here was key to this deal. 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 tenth in our first season back in the Premier League but it has paid off by him choosing us."