The 24-year-old completed a club-record transfer to the Hammers earlier in the week after spending last season at Upton Park on loan from Liverpool.
The former Newcastle forward has nine England caps to his name, with the last coming as a substitute in the 5-0 win over San Marino in October.
West Ham boss Sam Allardyce has already backed Carroll to break back into Roy Hodgson's squad and, with World Cup qualifiers against Moldova and Ukraine in the opening weeks of the new season, the player himself is also targeting a return from international exile.
"I want to keep fit, score goals and perform week-in week-out," he told the club's official website. "If I do that hopefully I'll get into the England team. If it comes with England, then it'll come."
Carroll also wants to taste success at club level and is hoping his blossoming relationship with Allardyce can see him add to his npower Championship and League Cup winners' medals.
"Every footballer wants to win trophies too and I don't see why we can't the way our team is going," he added.
"Sam is a great manager and a great man. I enjoyed working under him at Newcastle and here too, so speaking to him over the summer, he was happy with the way I was last season and I'm looking forward to working with him again.
"It's always good when you have somebody who is behind you. He only gives me confidence to go out there and show what I'm about."
Carroll penned an initial six-year deal at West Ham on Wednesday after a largely unfulfilled time at Liverpool, who shelled out £35million to take him from Newcastle in January 2011.