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McGeady is the first player to win both awards in a single season since former team-mate Shaun Maloney in 2006.
"Obviously I am delighted. I've got to give thanks to the players who voted for me," he said.
"I think my game's come on an awful lot with the help of the coaching staff and the players I'm playing with, but I think the main thing is consistency."
The Republic of Ireland international played a key part in Celtic's European and domestic campaign this season.
McGeady scored his first Champions League goal earlier this season, the only goal in the 1-0 win over Benfica in November.
The 16-times capped midfielder has also scored eight goals in the Scottish Premier League as well as providing a number of assists.
Hamilton Accies won promotion to the SPL at the weekend and Reid said: "It's been a fantastic 24 hours for me.
"The big thing for me was obviously getting to the Premier League and this award caps it off.
"I didn't play in the SPL as a player so I've got a chance to do that as a manager and I can't wait."