The 24-year-old finalised what is understood to have been a £15.5million deal, plus a further £2million in add-ons, from Liverpool on Wednesday after passing a medical the night before.
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.
The signing of Carroll is a clear indication of the east London club's desire to build on a creditable 10th place last season as they retained their top-flight status under Sam Allardyce, and will begin the new Barclays Premier League campaign at home to newly-promoted Championship winners Cardiff.
West Ham were moments away from winning the FA Cup in 2006 before a dramatic equaliser from Steven Gerrard forced extra time and Liverpool went on to win a penalty shoot-out.
With the Irons set to take up tenancy in the revamped 54,000-seater Olympic Stadium for the start of the 2016/17 campaign, Carroll is in no doubt he has signed for a club very much on the up.
"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 can't wait."
The move 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 £35million 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 which prompted a temporary switch south.
West Ham have already moved to strengthen the squad with the signing of veteran Romania captain Razvan Rat, the defender moving on a one-year free transfer deal as well as goalkeeper Adrian on a free transfer from Real Betis.
Several players have, though, also been released, among them former England frontman Carlton Cole, whose agent claims has received offers from the Premier League as well Europe and Major League Soccer in the United States.