The Senegal international joins for an undisclosed fee and becomes the club’s second summer signing following the recent arrival of Argentine striker Mauro Zarate.
A number of clubs were thought to be tracking the 24-year-old, but he was impressed with the perseverance of Sam Allardyce, who cut short his holiday to complete the deal.
Kouyate, who has played in the Champions League with the Belgian champions, 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."
Joint-chairman David Sullivan believes this latest arrival proves the club are serious about launching an assault on the top half of the Premier League after the struggles of last season.
He hopes for at least four more recruits during the summer before the opening game against Tottenham at Upton Park.
"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," said Sullivan.
"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."