The Algerian has been a solid performer in his debut season at Ibrox, helping the club to second place in the SPL, just a point off leaders Celtic with four games remaining.
Bougherra, a £2.5million signing from Charlton last summer, has played 34 matches for the Light Blues this season and has been the cornerstone of the meanest defence in the Scottish top flight.
The 26-year-old admitted his delight at receiving the award, which is voted for by the club's supporters.
"It was a surprise to me that I won because the likes of Steven Davis, Pedro Mendes and big Davie Weir were all in contention," Bougherra said.
"Allan McGregor and Kris Boyd were there too and each one of those players could have won it instead of me.
"I am very pleased because if the fans vote for you to win, it means you have done very well.
"I've given everything for the team and I want to win the title.
"This is the biggest night of my career. When you win trophies like these, you have more motivation to win the title with the team as well."
Midfielder Steven Davis missed out on the top award but was nevertheless recognised by his team-mates as he took home the Players' Player of the Year award.
"I'm really chuffed," said Davis.
"It's really good to have your fellow professionals voting for you like that.
"I've put a lot of effort in throughout the season and I'm really pleased they recognise that."
Midfielder Pedro Mendes received the award for goal of the season for his effort in the 4-2 win over Celtic in August, while Kris Boyd received the Sam English Bowl as the club's top goalscorer and John Fleck retained the Young Player of the Year award.
Rangers 13/10, Celtic 15/8, Draw 11/5