The 24-year-old has finalised what is understood to have been a £15.5million deal, plus a further £2million in add-ons, from Liverpool after passing a medical on Tuesday evening. Carroll, whose six-year deal could be extended by a further two, enjoyed his loan spell at Upton Park last season, scoring seven times in 24 league appearances.
"I am going to give it my all, to hopefully get some more goals and the aim is to win something, and I can't see why we can't do it with the way the team is going," Carroll said on West Ham TV.
"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 is being run, obviously getting the new stadium and everything like that, it is only going up, and that is what I want to be a part of.
"It is going to be even better there when even more fans can fit in and I cant wait."
With the Irons set to take up tenancy in the revamped 54,000-seater Olympic Stadium for the start of the 2016/2017 campaign, Carroll is in no doubt he has signed for a club very much on the up.
The deal brings to an end a largely disappointing spell of the centre-forward's career at Anfield, where he never really made a major impact following a high-profile £35m on transfer deadline day from Newcastle in January 2011.
Carroll scored 11 times in 58 appearances for the Reds, but when manager Kenny Dalglish was replaced by Brendan Rodgers last summer it became apparent his chances of regular first-team football would be minimal.