The Russian outfit have been pitted against the Scottish champions in Group G, which also includes Barcelona and Benfica.
"I'm delighted with the draw and it will be great to be back," McGeady told Celtic's official website.
"I've been back a few times to Celtic Park as a fan to watch games, so to go back as a player will be a different experience, but it's one that I'm looking forward to.
"I'm still in contact with people at the club and I've still got friends at the club but it will be strange going into the away dressing room. That's where I used to get changed up until I was about 18, when I was in the reserves."
McGeady further highlighted his love for Celtic by saying that they are "[his] team".
"But I still follow the team and keep up-to-date with how they're doing because Celtic are still my team," said the 26-year-old.
"I grew up supporting them and they're the team I grew up in."
McGeady joined Spartak from Celtic in August 2010.