The 23-year-old arrived in London on Saturday to complete his medical and his transfer is set to be announced on Monday.
There was plenty of interest from other Premier League clubs for Kudus, with Brighton & Hove Albion even reaching an agreement in principle with Ajax.
However, the Hammers also made a move, and they are now on the verge of signing him.
He has seen a massive increase in his stock after producing some excellent displays for the Dutch giants last season.
Kudus made 30 appearances in the Eredivisie last term, scoring 11 goals and registering four assists.
The Ghana international also featured in six Champions League matches, netting four goals.
He averaged an impressive 2.3 shots, 1.0 key passes and 3.0 dribbles per game in the Dutch top flight (as per WhoScored).
Kudus is mainly used as an attacking midfielder, but he is also capable of playing as a winger or a centre-forward.
He is highly rated for his dribbling, tackling and finishing ability.
West Ham made a slow start to their transfer dealings, but they have now made some excellent acquisitions in the last few weeks.
The Hammers signed Edson Alvarez before completing moves for James Ward-Prowse and Konstantinos Mavropanos.
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