Previously linked with Arsenal and Liverpool, the 24-year-old defender moves to East London on a four-year contract, becoming the club's second signing of the summer following Mauro Zarate's arrival.
Kouyate heaped praise on Sam Allardyce for abandoning his holiday to ensure that the deal went through.
"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," Kouyate told the Hammers' website.
"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."
Kouyate, a Senegalese international, appeared in all 38 league games for Anderlecht last season, scoring once.