The 24-year-old completed his move to the London club on Wednesday after impressing on loan at Upton Park last season.
The former Liverpool man struggled to start under Brendan Rodgers and hopes that a permanent move will assist his chances of playing for England at the World Cup in Brazil in 2014.
"My aim is keeping fit, scoring goals and performing every week," Carroll said in the Daily Mail.
"If I do that I'll hopefully get in the England team. It's always important to play football for your country. If I play well and keep fit, I'm going to be playing every week. If it comes, England will come.
"Sam's [Allardyce] a great manager. It's always good when you've got somebody behind you. He gives me confidence to show what I am about."
West Ham start their Premier League campaign with a home game against Cardiff City.