Sky Sports News says an agreement is all in place for the Anzhi Makhachkala man who will join for a reported fee of £30 million with the player telling the channel he will finish his medical on Thursday.
Earlier on Wednesday, Andre Villas-Boas confirmed that Tottenham were in talks with Anzhi Makhachkala over the signing of the Brazilian.
"I can't really confirm anything regarding Willian. There is interest in the player and there have been conversations," Villas-Boas said at a press conference prior to Tottenham's Europa League play-off against Dinamo Tbilisi.
Villas-Boas declared his appreciation for Willian on Monday and he has moved quickly in his attempts to sign the player following interest from Liverpool.
Should Willian pass his medical and sign for Tottenham, for a fee of around £30million, the north London club will break their transfer record for a third time this summer.
Spurs have already spent £60million on new players this summer, but their manager hopes to strengthen his squad further.
"We will see some new players in defence and attack," Villas-Boas said.
Villas-Boas declined to comment on the prospect of signing Roma midfielder Erik Lamela and Real Madrid defender Fabio Coentrao, who have been linked with the club.
"They have not signed for Spurs. Both of them are great, great players, but I cannot extend myself," he said.
Real Madrid target Gareth Bale has not travelled to Tbilisi because of a foot injury while Sandro, Jan Vertonghen and Aaron Lennon will also not feature because of injury worries.