The 24-year-old, who won the title with the Belgian side last season, becomes Sam Allardyce's second summer signing following the arrival of Argentine striker Mauro Zarate earlier in May.
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"I am very happy, because today West Ham have given me the chance to play in the Premier League," he told West Ham TV. "So I'm very happy to join such a club and that gives me great pleasure.
"I know a few players who were also at the club, [Carlos] Tevez, Demba [Ba], Andy Carroll, who was obviously here last season. West Ham are a team who are known and who are going to help me to progress. For my part, I'm going try to do great things here and try to improve further still as a player.
"That I'm here now is thanks to the manager, because he went out of his way, leaving his holiday for me, so he has done everything he could for me to join the club.
"He, my advisors and agents helped me make the right decision and said West Ham was the ideal club for me, because as a kid I dreamed of playing in the Premier League and now it's here that my dream has been realised."
And while joint-chairman, David Sullivan, has expressed his delight at clinching the signing of the player ahead of rival clubs, he hinted the side are still in the market for ‘at least four more signings’.
"I am absolutely delighted to have clinched the signing of Cheikhou after weeks of tough negotiations that saw us beat off the challenge of some huge clubs across Europe for his signature," he said.
"He comes with vast experience at the top level - including the Champions League - despite being only 24 and I am sure he will add valuable competition to places.
"We are determined to have a better season this year and this signing is a statement of the direction the club is heading in. We hope to have at least four more signings in place by the time we kick-off against Tottenham on 16 August as we aim for at least a top-ten finish this season."