Manager Neil Lennon hailed it as "one of the greatest nights in the club's recent history," while Parkhead legend Henrik Larsson described the surprise victory as Celtic's best ever European result (via the Telegraph and BBC). Die-hard fan Rod Stewart, meanwhile, was reduced to tears.
The Bhoys, however, are no strangers to securing impressive results on the continental stage.
Here are Celtic's top five European triumphs.
It's fair to say that 1967 was a rather good year for the Bhoys.
Led by legendary manager Jock Stein, Celtic won the Scottish League, the Scottish Cup, the Scottish League Cup, the Glasgow Cup and most significantly, the European Cup.
After progressing through four rounds, the Hoops met Internazionale at the Estádio Nacional in Lisbon in the final. The Italians, who had already won the tournament twice at that point, took the lead with a seventh-minute penalty, but second-half goals from Archie Gemmell and Stevie Chalmers were enough to make Celtic the first British European Cup holders.
Celtic made the European Cup Final once again in 1970 but were unable to overcome Feyenoord at the San Siro.
Celtic's European prowess of the late 1960s and 1970s began to decline as the 1980s rolled around but not before they pulled off a famous victory against a Spanish giant.
For the first leg of the European Cup quarter-finals of 1979-80, a Real Madrid side featuring Vicente del Bosque and Englishman Laurie Cunningham visited a Celtic Park filled with the noise of 67,000 Hoops fans.
Afer a tense first half, George McCluskey opened the scoring on 52 minutes, with winger John Doyle heading a second in the 75th.
Unfortunately, the 2-0 lead wasn't enough to take into the second leg, where Los Blancos triumphed 3-0.
Celtic lost their opening group match of the 2006-07 Champions League to Manchester Utd at Old Trafford in a thrilling 3-2 tie.
Yet the Scots knew they would be able to qualify for the knockout stages for the first time in the Champions League era if they earned three points when the Red Devils visited Parkhead in the penultimate group game.
A full-strength Utd side made few opportunities on the evening and suffered their second consecutive 1-0 away defeat of the group stage when Japanese midfielder Shunsuke Nakamura buried a sublime free kick.
Celtic were narrowly beaten by a Kaka injury time goal when they faced Milan in the first knockout round, and the Italians went on to knock Alex Ferguson's side out in the semi-finals.
When reigning European champions AC Milan visited Parkhead in the 2007-08 Champions League, few expected the Italians to leave with anything but three points.
However, after an uneventful first half, Stephen McManus gave the Celts the lead when Milan failed to adequately defend a corner. Kaka brought things even with a penalty six minutes later, but Scott McDonald helped the Scots claim a huge European scalp with his 90th-minute effort.
While McDonald celebrated the goal with his team, Milan goalkeeper Dida received a tap on the shoulder from a fan and proceeded to pull off one of the worst dives of all time.
The surprise win helped Celtic qualify from their group, but they and Milan were eliminated at the first knockout stage by Barcelona and Arsenal respectively.
After nearly earning a point at the Nou Camp with just 26 percent possession and defensive tactics that were roundly condemned in the Spanish press, Barcelona were expected to secure a win much earlier than the 94th minute in the return game at Celtic Park.
However, thanks to a phenomenal display from keeper Fraser Foster, goals from Victor Wanyama and Tony Watt and tactics that kept Leo Messi and his colleagues under wraps for most of the game, Celtic pulled off a famous victory against the Catalans.
This isn't the first time the Bhoys have overcome the Blaugrana: an Alan Thompson goal gave the Scots a 1-0 win in the fourth round of the 2004 UEFA Cup, which proved enough to earn them a spot in the quarter-finals on aggregate.