Questions had been raised over whether the playmaker would fit into the new manager's system, with the Portuguese having made attacking midfielder Gylfi Sigurdsson his first signing after taking charge.
The Netherlands international has been strongly linked with a move to former club Hamburg but, with Luka Modric seemingly edging closer to an exit, the 34-year-old says he wants to keep Van der Vaart.
“With Van der Vaart, at the moment I am absolutely counting on him,” Villas-Boas told The Sunday Telegraph.
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“We have to make sure the club's interests are met, and it's up to the chairman to decide that.”
Tottenham finished fourth twice during former boss Harry Redknapp's reign and the Englishman insisted that the club should go on to challenge for the title under his successor.
And Villas-Boas' says he is using the 65-year-old's words as motivation for his players, even though he says chairman Daniel Levy has not made such demands.
The ex-Porto boss continued: "Harry said last year that Tottenham could go on to win the title, and we have to take that on if we want to go forward as a club.
"That is basically the challenge I have put to the players, although it is not a challenge the chairman has put on to me.
"But the chairman wants continual success and that can only happen when you put trophies in your cabinet and hopefully we can do that.
"The club must be in the top four, and for us to bridge the gap to the title is a tremendous step, but it is one that the club is willing to make based on what Harry built from last year.
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Villas-Boas' also went on to express his belief that he can be a success at White Hart Lane, despite following the widely popular Redknapp.
"A good start is always very important," he added. "The departure of Harry might leave some fans reluctant, as always happens when you have managerial changes, because people [managers] create empathy and success.
"This club recognised Harry's success, but eventually decided to make changes and I was appointed. I want to make sure we move forwards rather than look backwards, and winning games is the best way to win over the fans."