Neil Lennon's side qualified for this season's group stage by the narrowest of margins, their 3-2 (aggregate) win against Shakhter Karagandy granting them passage to the final 32.
It was "the greatest thing I've ever done in football," Lennon told the BBC.
They have been drawn in another particularly tricky group this season, with Ajax, Barcelona and AC Milan making up Group H.
The Hoops were somewhat an unknown quantity last term, profiting from their set-pieces that found the likes of Barcelona unawares. This season, they might not sneak under the radar in quite the same way.
Below we look at key information for the tie and discuss some of the tactics the two teams may employ.
Celtic's New Bhoys
Lennon lost some of his prized players during the transfer window, with Victor Wanyama heading to Southampton and Gary Hooper signing for Norwich.
However, the Bhoys spent well and saw a clutch of new players arriving at Parkhead over the summer months. The addition of Teemu Pukki will be crucial for the side's chances in Europe. The 23-year-old former Schalke striker scored on his debut for Celtic last weekend and his pace will be a useful weapon against a slow AC Milan side who are missing some of their best players.
Derk Boerrigter also joined from Ajax last month. The left winger already has experience in Europe and his speed down the left flank could be vital for the Celtic counter-attack as they try to record their first win on Italian soil.
AC Milan's Injury Woes
The hosts are missing several key players. In defence, Matias Silvestre, Daniela Bonera, Ignazio Abate and Mattia De Sciglio are all sidelined.
In midfield, Kaka has been ruled out with a thigh strain and Andrea Poli and team captain Riccardo Montolivo have both been ruled out for a month. Up-front, Stephan El Shaarawy is a doubt after picking up an injury last week.
Massimiliano Allegri's side are looking increasingly threadbare and will be forced to field a makeshift starting XI.
"We'll make do with who we have," Allegri told the club's official website.
After last season's set-piece success, Celtic have earned a reputation as a long-ball team in Europe, reliant on corners and free-kicks.
However, it looks like the they have been working on playing the ball on the ground and have added much-needed width to the squad with the acquisition of Boerrigter. Pace will be key against a Milan side not noted for their speed. Lennon told the Daily Record:
Pace is very important in the Champions League and we've got that with Boerrigter. It is something we really focused on last year, particularly defensively.
Boerrigter is an interesting one because we haven't had a quick left-sided player for a while and he is prepared to go in behind people.
If he's fit and flying he'll be useful on the counter-attack in Europe.
He has the European experience as well. Teemu Pukki is very experienced at international and club level and will be a good player for us.
The Italian players know every trick in the book so it will probably be the same as last season. But we will know the way they play better than we did before we faced Juventus.
Do we need to be more streetwise? Absolutely, if someone holds you, you need to be strong and push them away before the set-piece is taken.
Will Celtic get their first win on Italian soil this Wednesday?
With barely anyone at the back for AC Milan and with a weakened midfield, Celtic will be able to take their chances and impose themselves at the San Siro.
Mario Balotelli—Milan's Key Man
AC Milan come into this game on the back of a loss, a win and a draw in Serie A.
A thoroughly unconvincing performance against Torino at the weekend almost ended in defeat for the Rossoneri, whose blushes were only saved through an 87th minute goal from Sulley Muntari and a penalty in the last minute of normal time from Mario Balotelli.
The Italian is undoubtedly Milan's best player at the moment and, if Celtic can stifle his impact, they will stand a really good chance taking at least a point from this game.
With Kaka, El Shaarawy and Montolivo all out of action, the supply line and support for Balotelli will be noticeably weaker. Celtic may even enjoy long spells of possession, something that did not happen when they took on Barcelona last season.
Defender John Kennedy has hinted that provoking Balotelli might be one of Celtic's tactics. He was quoted on ESPNfc.com, as saying: "You would try and upset him because on his night he is a handful for anyone. He has been (upset) in the past but it's important you don't get too caught up in trying to upset someone else"
Celtic Injury List
According to BBC Sport, Celtic will be without winger James Forrest (sciatica), with Joe Ledley also a doubt. Steven Mouyokolo will also be missing, the centre-back having sustained an Achilles injury that will see him ruled out for six months, as seen in the Daily Mail.
Allegri was quoted in the Daily Record admitting that his side cannot afford to slip up against Celtic. He said: "We are light in defence for the Celtic match and can't afford to make any mistakes."
His side may be missing a whole host of injured players but Allegri does have some aces in his deck. Over the summer the Rossoneri brought in Alessandro Matri from Juventus, who scored twice against Celtic in last year's competition.
Milan will probably field Balotelli, Robinho and Matri up-front, which isn't to be sniffed at.
Nigel de Jong and Muntari add steel in midfield and, while defender Philippe Mexes lacks pace, he is capable of scoring the occasional wonder-goal, such as this strike against Anderlecht last season.
AC Milan: Abbiati, Zaccardo, Zapata, Mexes, Emanuelson, Muntari, De Jong, Nocerino, Balotelli, Robinho, Matri
Celtic: Forster, Lustig, Van Dijk, Ambrose, Mulgrew, Matthews, Brown, Commons, Boerrigter, Samaras, Stokes