The Parkhead side will face Barcelona, who they famously beat last season, along with two former Champions League winners AC Milan and Ajax in Group H.
The draw for the group stages of football's most lucrative club competition followed Celtic's dramatic 3-0 second-leg play-off victory over Shakhter Karagandy on Wednesday night.
As reported in later editions of last night's Evening Times, the last gasp qualification goal from James Forrest means a £15million cash bonanza for Celtic.
The Parkhead side overturned a first-leg 2-0 deficit, and will now aim to better their achievements of last season when they emerged from a group containing Barcelona, Benfica and Spartak Moscow to go on and meet Juventus in the last 16.
Celtic manager Neil Lennon said last night: "I think it is the best and the worst draw we could have got.
"In terms of glamour I don't think it comes any better than Barcelona, Ajax and AC Milan.
"In terms of football it is probably the most difficult group we could have got.
"But I think the hard work was really done last night and we can go and enjoy the tournament now."
Celtic said dates, kick-off times and ticket details will be published when finalised and information on travel packages will be announced by the club on Sunday.
Glasgow is set to cash in, with visitors expected to pour into the city for what promise to be memorable nights of European action featuring some of the biggest names in world football.
Stuart Patrick, chief executive of Glasgow Chamber of Commerce, said: "Celtic's qualification for the Champions League group stage is great news for Glasgow.
"From a tourism point of view, it is ideal that they have drawn clubs from easily accessible and wealthy countries like Spain, Italy and Holland.
"We can expect a big influx of supporters who will boost the tourism and retail sectors."
And a spokesman for Glasgow Airport said: "Celtic's progress to the group stages of the Champions League is great news for the city and for the airport.
"Barcelona, Ajax and AC Milan are renowned for their fantastic fan base and we are looking forward to welcoming the thousands of supporters who will descend on Glasgow."
In travel terms for the Celtic support, last night's draw was a kind one.
Instead of arduous trips across the Continent, as in the qualifying round when fans had to make the journey to far-flung Kazakhstan, this time they'll be heading to some of Europe's most cosmopolitan cities.
The possible down side is the stature of the teams they'll face when they get there.
Barcelona not only feature their talismanic wizard Messi among a host of football's biggest stars, they have made arguably the most spectacular signing of the summer in the Brazilian protege Neymar da Silva, picked up for a cool £48.6m.
Celtic must also travel to the infamous San Siro in Milan where a tough test awaits in the form of seven-times Champions League winners AC Milan, featuring the at times combustible Italian striker Mario Balotelli.
And on top of that is the trip to Amsterdam to take on 1995 Champions League winners Ajax.
But after Celtic stunned the footballing world by beating overwhelming favourites Barca at home when the sides met last season, Celtic will fancy their chances against anyone on home turf.
The other groups will see Arsenal face last season's runners-up Borussia Dortmund, Rafael Benítez's Napoli and Marseille.
Manchester City will play reigning champions Bayern Munich, CSKA Moscow and Viktoria Plzen.
Chelsea tackle two sides they conquered en route to last year's Europa League title in Basle and Steaua Bucharest, plus Schalke.
And David Moyes's Manchester United will meet Shakhtar Donetsk, Bayer Leverkusen and Real Sociedad.