The 24-year-old received this latest honour after another impressive season for club and country and he moves level with fellow three-time winners John Hartson and Mark Hughes.
Bale's outstanding performances have earned plenty of plaudits and earlier this year he won the Professional Footballers' Association and Football Writers' Association Player of the Year awards.
The attacker scored 26 goals in all competitions for Tottenham before linking up with Real Madrid in a world-record move and continues to be a crucial player for Wales.
He tweeted: "It's a great honour to receive the Fans Player of the Year and Player of the Year @FAWales awards. Can't wait to get back playing again soon."
Bale, who is currently sidelined by injury, also received the Fans' Player of the Year award, and Wales boss Chris Coleman was full of praise for him.
He said: "Gareth's definitely one of the best players I've seen. I've had the fortune of being up close and personal with him in training and he's a player that can take your breath away.
"In two or three seconds, he will do something that nobody else can do. He's a special player.
"He's serious about Wales, he's a Cardiff boy and patriotic and what he does for Welsh football is raise the interest in football for our country. He's brought that for us.
"He's a great player - and I still think he's getting better because of his age. He'll only get better working under a manager like Carlo Ancelotti and playing for Real Madrid with players like Cristiano Ronaldo."
Swansea left-back Ben Davies secured the Young Player of the Year prize, while his team-mate Ashley Williams was the Club Player of the Year for the fourth time.