Wales international Bale picked up the Player and Young Player of the Year awards on Sunday to round off a remarkable season.
The 23-year-old, who has scored 19 goals in 29 games for Spurs this term, became the first player to do the double since Cristiano Ronaldo.
Villas-Boas feels the decision was justified after watching Bale develop during the Portuguese manager's debut season at White Hart Lane.
He told Sky Sports: "The player has been amazing, really dedicated to his job, to what he's been doing.
"For the amazing year that he's had he deserves to collect both awards."
Bale beat off competition from Manchester United frontman and Premier League top scorer Robin van Persie, who won last year, to scoop the main award.
Van Persie came in third this year behind Bale and Liverpool frontman Luis Suarez, currently second-top scorer in the league.
Asked if beating those two to the prize made the feat even more special for Bale, Villas-Boas added: "I think so. His form has been outstanding.
"For a player who has developed so much in a year, this type of recognition comes at the right time and (is) full of merit. I'm extremely happy for him."