Carroll completes record breaking West Ham move - club
The Hammers said on whufc.com that the 24-year-old, who was on loan at the club last season, had signed a six-year contract, with the option of a further two.
No transfer fee was disclosed but it was reported that Carroll cost West Ham a club record £15.5 million (18.1 million euros, $24.3 million), plus a further £2 million in add-ons.
Carroll, who played under manager Sam Allardyce at Newcastle United, turned out 24 times and scored seven times for West Ham last season but was plagued by injury.
"It's fantastic for me to be here. I really enjoyed last season, and that shows in me coming back and making it permanent," he was quoted as saying.
"The fans, the lads and the club itself has 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."
Carroll began his career at his local club Newcastle in 2006 and scored 19 goals in the 2009/10 season helping the Magpies win promotion from the second-tier Championship at the first attempt.
Liverpool played a club record £35 million in 2011, making him the most expensive British player but despite that he never fitted in on Merseyside.
He has won nine England caps and scored twice for the national side.
Liverpool, for whom Carroll played 58 times, scoring 11 times, also confirmed the move and said in a statement: "Everybody at Liverpool FC would like to wish Andy all the best for the future."
Anfield boss Brendan Rogers has been keen to bring in new players. He has already signed Manchester City defender Kolo Toure and Celta Vigo forward Iago Aspas.
Carroll is West Ham's third signing of the close season. Allardyce has already brought in Shakhtar Donetsk's Romania defender Razvan Rat and Real Betis goalkeeper Adrian.
Related West Ham United News