The 24-year-old is expected to undergo a medical on Thursday before signing a six-year contract.
Spurs reportedly had a £50m offer rejected by West Ham, before an improved bid was made.
Kudus, who scored five goals and got three assists for the Hammers last season, is under contract until 2028 and has a reported buyout clause of £85m for Premier League clubs.
The Ghana international has impressed since moving to England from Ajax in 2023, scoring eight goals and providing nine assists in his debut campaign for West Ham.
A new forward has been a priority for Tottenham this summer, with speculation of interest in Brentford’s Bryan Mbeumo, who is a top target for Manchester United.
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All Angles: Spurs celebrate after ending long wait for trophy with Europa League triumph
Video credit: TNT Sports
Instead, Spurs have turned to Kudus, who looks set to make the short move to north London and join up with new head coach Thomas Frank.
Manchester City v Tottenham Hotspur to be shown live on TNT Sports
Manchester City’s clash with Tottenham Hotspur is one of three big Premier League games live on TNT Sports in August, along with a mouthwatering west London derby.
Tottenham will travel north for their first away league game under new boss Thomas Frank.
Live Premier League games on TNT Sports in August
| SAT 16TH AUG | ASTON VILLA V NEWCASTLE UNITED | 12:30 |
| SAT 23rd AUG | Manchester City in Tottenham Hotspur | 12:30 |
| SAT 30th AUG | Chelsea in Fulham | 12:30 |