West Ham co-chairman David Gold confirmed the player had passed the medical ahead of a £15 million move.
Carroll spent last season on loan from Liverpool at Upton Park but had delayed making a decision on whether to move permanently.
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The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.