The Anzhi Makachkala midfielder is believed to have passed his medical in London ahead of his proposed move, which would make him Spurs' third record signing this summer after deals of £17m and £26m for Paulinho and Roberto Soldado.
Tottenham could recoup all of their outlay so far if they accepted Real Madrid's world record offer for Wales forward Gareth Bale though the club refused to comment on reports in the Italian and Spanish media that technical director Franco Baldini was in Madrid for discussions over the transfer on Wednesday night.
Willian had been linked with a move to Liverpool but appears to have been lured by the guarantee of European football at White Hart Lane this season.
Spurs could yet add Roma striker Erik Lamela to their ranks in a transfer that would take their outlay during this window to almost £120m.
Portugal left-back Fabio Coentrao has also long been mentioned as a possible makeweight in any deal for Bale.
Speaking about Coentrao and Lamela at a press conference ahead of Spurs' Europa League game against Dinamo Tbilisi, Villas-Boas said: "They have not signed for Spurs. Both of them are great, great players, but I cannot extend myself."
Meanwhile, ousted Anzhi Makhachkala boss Rene Meulensteen believes Spurs will have landed "a major trump card" if they push through a deal for Willian.
"I've worked with him for a short time but I really, really like him. He will be an asset for whoever's going to get him," said Meulensteen on Sky Sports News.
"If it's Spurs that's going to get him they'll get an excellent player. He's very versatile, he can play in different positions, he's a very creative player and an excellent professional with a very good personality.
"He's going to be a major trump card for Spurs if they can get the deal to go through.
"He can beat a player, he can score a goal. I thought he was an absolute delight to work with."