The award was part of a double for Blair who also captured the Celtic League player of the season prize.
Meanwhile, his Edinburgh and Scotland team-mate, hooker Ross Ford, won the award for Try of the Season with his glorious score against Leicester Tigers in the European Cup at Murrayfield.
Blair said: "It's been a fantastic year for me.
"I always say that it's an honour to play for Scotland but to captain Scotland in this season's Six Nations was a dream come true.
"To win both the Magners and Scotland player of the season in the same year just caps off an excellent season for me."