Palace confirmed the reported £9.5million deal on Wednesday, with Kouyate arriving on a four-year contract.
Kouyate – who featured for Senegal at this year's World Cup – swapped Belgian giants Anderlecht for West Ham in 2014, the 28-year-old scoring 12 goals in 129 appearances for the Hammers.
"I'm so happy. It's been a long day but now everything is good and I'm very excited to start with my new team-mates," Kouyate told Palace TV .
"This is the right time to move because I needed a new challenge. I have good memories of West Ham but I need to come here and give my best because I like the Crystal Palace project.
"I spoke to the manager and I know he'll be a good manager. I also spoke to Pape Souare yesterday and he told me I had to come and now I'm here and I'm very happy."
Kouyate's signing comes as Roy Hodgson's Palace reportedly close in on one of the biggest coups of the transfer window, with former Schalke midfielder and German star Max Meyer poised to join on a free transfer.