Carroll added: "The fans, the lads and the club itself have been great to me, and what I wanted to do was come back here and play football.
"Since the end of the season I've had a lot of time to think, I've missed it and that's why I'm back.
"Getting promoted the season before last, then finishing where we did - we did great, and it can only get better for us.
"The way the club's being run, obviously getting the
and everything like that, it's only going up."
Andy Carroll is one of the most expensive English players in the history of football - during his career his transfer fees have reached £50m.
Other notable expensive English players include (total fees):
(Aston Villa): £53.5m
(Stoke City): £50.6m
(Manchester United): £48.5m
(Manchester City): £41.6m
Carroll suffered a number of injuries during his time on loan at Upton Park, with
problems keeping him out of action for several months.
He also picked up a heel injury on the final day of the season after landing awkwardly, with the knock keeping him out of the England squad for the post-season friendlies against Republic of Ireland and Brazil.
Carroll believed he could play his way into England manager Roy Hodgson's plans if he could improve on his fitness record next term.
"I just want to keep fit now, keep scoring goals and performing week in and week out for West Ham, if I do that here, play well and keep fit, then hopefully I will get in the England team," Carroll said.
Carroll, who made his England debut in 2010 and has won nine caps, was signed by Kenny Dalglish for Liverpool on transfer deadline day in January 2011, for what remains a record fee for a British player.
He had impressed by scoring 31 times for his boyhood club Newcastle in 81 appearances, but his time at Anfield was short-lived.
Coupled with the arrival of Brendan Rodgers and a new style of play, Carroll's return of just six goals in 44 league outings for Liverpool saw him loaned to West Ham.
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