Bale was in scintillating form for both Tottenham Hotspur and Wales last season, scoring 31 goals in 53 appearances for club and country.
That form prompted Real Madrid to part with a world-record fee of £85m to secure his signature this summer, although his early career in the Spanish capital has been interrupted by injury.
The 24-year-old was also named the Fans' Player of the Year, and manager Chris Coleman backed him to get even better at Madrid.
"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," Coleman said at the ceremony.
"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."