The Brazil forward will join the north London club from Everton for an initial £50million, with a potential further £10m in add-ons.
Arsenal and Chelsea had both shown an interest in the Brazilian, but Spurs moved swiftly to wrap up an agreement for the 25-year-old.
He agreed personal terms earlier this week and will undergo a medical on Thursday [June 30].
Bill Kenwright and Daniel Levy, the chairmen of Everton and Tottenham respectively, were spotted having dinner over the weekend and Richarlison was likely the main topic of conversation.
He joined the Merseyside club from Watford in 2018 and netted 53 times in 152 games.
Last season, he scored 10 Premier League goals to help keep the Toffees in the Premier League.
June 30 is also a significant date, because that is when the financial year for football clubs end.
Everton have lost £372m over the last three years and need to balance the books.
Tottenham have been swift with giving manager Antonio Conte new signings this summer and he has been backed by chairman Levy.
Yves Bissouma has joined from Brighton for an initial £25m, while Ivan Perisic and Fraser Forster have signed on free transfers.
Spurs are also close to a deal to sign defender Clement Lenglet.
The France international centre-back, 27, is set to join on loan from Barcelona for the season.
The next name on the list for Conte is set to be Middlesbrough full-back Djed Spence.