Kudus has signed a five-year contract at the London Stadium with the option for a further 12 months.
The 24-year-old is West Ham's fourth summer signing and their second recruit from Ajax for the new season.
Mexican international Edson Alvarez joined from the Dutch giants earlier in the transfer window while James Ward-Prowse and Konstantinos Mavropanos have switched from Southampton and Stuttgart respectively.
In his three full seasons with Ajax, Kudus won two Dutch Eredivisie titles and scored 27 goals in 87 appearances, including a hat-trick against Ludogorets in the Europa League in his final game last week.
"I've been dreaming to play in a league like this since I was a kid," said Kudus, who will wear the No 14 shirt at West Ham.
"I've been dreaming of this moment and I'm so happy to be here. But it doesn't stop here, I want to keep going.
"I try my best to entertain the fans as I think that's what football is all about. I'm just here to do my best and help the team. I'm really happy to be here. I will fight for the badge. I can't wait to get started."
West Ham boss David Moyes added: "I'm delighted we've been able to bring Mohammed to West Ham United.
"He's a terrific young talent, who has already shone at the very highest level for Ajax in the Champions League and made well over 150 senior appearances at the age of 23 - so it was no surprise to see so many top clubs chasing his signature this summer.
"The fact we've been able to attract a player of his undoubted quality to London Stadium shows the pull West Ham have now - the board and Tim [Steidten, West Ham's technical director] deserve huge credit for getting this one over the line."
