Carroll completes loan move to West Ham
West Ham will then have the option of a permanent deal to sign Carroll for an undisclosed fee at the end of the season.
"It's great to be here at West Ham and all signed up - I just can't wait to get started now," the 23-year-old Carroll told the official West Ham website.
"I want to be playing games and obviously hoping to score some goals. I know the manager well and some of the lads, so it is nice for me to come to a place where I know people."
Carroll joined Liverpool from Newcastle United in January 2011 for a club record fee of 35 million pounds, replacing the Chelsea-bound Fernando Torres.
But he struggled to make the same impact he enjoyed in his native north east, scoring just 11 goals in 58 appearances for the Anfield club.
Carroll, who scored a fine headed goal for England against Sweden at this year's European Championship, said the chance of working again with coach Sam Allardyce had been a key factor in his decision to join the Hammers.
"I'm hoping to add a lot of goals and create a few chances. I know Sam from Newcastle and he was a massive reason for me coming," he said.
"When I worked with him at Newcastle it was great so it was a no-brainer really."
Allardyce was keen to stress that the new addition to his squad was more than just a powerful physical presence.
"I think for all parties this is a great signing," he said.
"Andy is an all-round footballer, but because he is six foot three inches and one of his strengths is his aerial power, everybody dismisses the ability he possesses on the floor."
Liverpool moved quickly to replace Carroll, completing the signing of Samed Yesil from German club Bayer Leverkusen.
The 18-year-old striker, who was in impressive form for Germany during the 2011 Under-17 European Championship, moved to Anfield on the recommendation of Leverkusen coach and former Liverpool captain Sami Hyypia.
"I am really happy about this, it is my dream to play for Liverpool and I will give my all," German Yesil told the Liverpool website.
"The first thing is that I have to train and then in one or two years I hope, step by step, to be in the first team.
"I will work hard here. I have read how the manager here will make a team that is young and that makes many passes, and I think I can be the right player for this."