Celtic supporter Reid, 60, is quitting as an MP at the next General Election, which many pundits reckon is imminent.
Reid, who has had nine ministerial roles in 10 years, said: "Brian Quinn has been a superb chairman and is an extremely hard act to follow.
"I have been a supporter of Celtic for many years and am delighted to be invited to join the board and carry on the great work that has already been done.
"Like every schoolboy who supported Celtic, I always dreamed of pulling on the hoops and scoring at Celtic Park. I never made it as a player but his is the next best thing."
