Kouyate has signed a four-year deal with the Hammers.
He told the club's official website: "I am very happy, because today West Ham have given me the chance to play in the Premier League. 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 to 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 advisers 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."
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