The London Stadium club have been working hard on a deal for Kudus and it seemed in the balance recently, especially with interest from clubs in Saudi Arabia.
Hammers technical director Tim Steidten has got the deal on track though and there is now a verbal agreement with Ajax based on a package of €45m plus a ten per cent sell-on clause.
Kudus has agreed to sign a five-year contract at West Ham.
The Hammers have even taken the step of booking Kudus in for a medical on Saturday.
They will hope to now quickly push the deal over the line and put the midfielder at the disposal of boss David Moyes.
West Ham are hoping to have the transfer documents to sign within the next 48 hours.
Landing Kudus is likely to be seen as a coup, with Ajax having been reluctant to part ways with him this summer.