Irish international winger McGeady spent six years at Celtic before moving to Russia in 2010 and he is excited about the prospect of facing Neil Lennon's team in the Group G match.
"I'm really happy to play against the club where I grew up as a professional footballer," McGeady said. "I came to Celtic at the age of 12 and the club is still in my heart.
"It will be terrific and thrilling for me to come onto the pitch of Celtic Park in December in the return match."
McGeady, 26, added that he expected a tough match on Tuesday against the young and ambitious Scottish Premier League leaders.
"Today Celtic are a young team who want to make themselves known. I expect a tight match on Tuesday as Celtic always battle up to the very end," he said.
Spartak and Celtic limbered up for Tuesday's match with confidence-boosting wins in their respective domestic leagues.
Nine-time Russian champions Spartak battled back from a goal down to clinch a 3-1 win over hosts Amkar at Perm.
The Moscow side's goals came from 30-year-old former Lyon midfielder Kim Kallstrom, Brazilian forward Ari, and striker Artem Dzyuba.
"It was a very important match for us," said Spartak's Spanish manager Unai Emery.
"We expected a tough battle and we've got it as Amkar haven't suffered a home defeat in the previous 12 months.
"Luckily we managed to battle back and gain three points and now we can concentrate on the match with Celtic."
Emery added that Spartak goalkeeper Adnrei Dykan has suffered a recurrence of his shoulder dislocation and is a doubt for the match with Celtic.
Spartak will also be without Brazilian midfielder Romulo, who underwent knee ligament surgery last week and will spend several months on the sidelines.
Celtic coach Lennon said he believed that his side's 2-0 win over Motherwell at the weekend will give his side confidence.
Celtic's two goals in three first-half minutes saw the Hoops leapfrog their hosts to the top of the SPL standings.
"Every one of them -- even the subs that came on -- were brilliant," said Lennon, who was delighted to see Georgios Samaras and Joe Ledley return from injury.
"It was great to see Samaras back in full flow again and it augurs well for Tuesday," Lennon said.
Spartak will try to gain revenge for their Champions League elimination at Celtic's hands in the 2007 season's third qualifying round, when they lost on penalties after two draws.
Celtic, meanwhile, must try to improve on their disastrous away record in the Champions League, as they have lost 19 of their 20 matches on the road since their first group-stage appearance in 2001.
Spartak gave Barcelona an almighty shock in their first group game this season when they led 2-1 until the last 20 minutes at Camp Nou, when the Catalan giants snatched a 3-2 win.
Celtic drew 0-0 at home to Benfica in their opener.
Source: AFP
Source: AFP