The 23-year-old, who has scored 24 goals in 40 appearances this season, is regarded as one of the hottest properties in Europe.
Manchester United and Real Madrid have both been linked with moves for the Welsh international, but Villas-Boas has confirmed that Bale will stay regardless of whether or not the club secure Champions League football this season.
"The information that I have from the club, which was mistakenly written about last week, is that the player is here to remain, independent of the objectives of Champions League qualification being achieved or not," Villas-Boas told reporters at a press conference.
"I would be extremely surprised [if he left]. In football anything can happen. It's impossible to predict, but this is the assurance I have had from the club.
"We understand that the more awards the more recognition the player will have, the more media attention, but the club has to move forward by holding onto its best players. With the recognition and the further experience that he has had from this year, next year for Tottenham he will be even more assertive."
Bale was named the Football Writers' Association Player of the Year earlier this afternoon.