The Blues confirmed the switch, subject to a medical, earlier today.
Willian completed a medical with Spurs and was on the verge of moving to White Hart Lane before Jose Mourinho pounced, but Villas-Boas has refused to criticise the 25-year-old.
"Willian made a choice to join Chelsea and I can only wish him good luck," Villas-Boas told reporters. "He is a person I have a good relationship with.
"Good luck to him. He made a choice, that he feels is important for the development of his career, good luck to him."
Willian moved to Anzhi Makhachkala from Shakhtar Donetsk in January.