The Welshman was named the PFA Player of the Year and also picked up the trophy for the Young Player of the Year, becoming only the third person to achieve the feat.
"The player has been amazing, really dedicated to his job, to what he's been doing," Villas-Boas told Sky Sports News.
"For the amazing year that he's had he deserves to collect both awards. 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."
Bale pipped second-placed Luis Suarez and Robin van Persie in third to the senior prize.