Neil Lennon's side advanced as group-winners despite a final-day defeat to CFR Cluj in Romania - their back-to-back wins over Lazio coupled with a draw and win over French side Rennes and 2-1 win over Dan Petrescu's side in Glasgow enough to seal top spot ahead of the last round of group games.
The Hoops will go into the draw as a seeded club, and could be paired with Nuno Espirito Santo's Wolves side in the Round of 32. They can't face CFR Cluj, having been in the same group, while country protection means the prospect of an Old Firm showdown in Europe isn't on the table until at least the round of 16.
Rangers are unseeded having progressed as runners-up in Group G and could face Arsenal or Man United in the knock-out stages. The Gers and Porto will be kept apart having been in the same group but Benfica and Braga could wind up being paired with Rangers.
WHO CELTIC COULD FACE
APOEL - The Cypriots finished as runners-up behind Sevilla in Group A, are 13 places below Celtic in the UEFA rankings and have never progressed past the round of 16.
AZ Alkmaar - The Dutch side were runners-up in 1980/81 and finished in second place behind Man United in Group L. They are ranked 37 places below Celtic.
Bayer Leverkusen - Ranked 28th, the Bundesliga side won the competition in 1987/88, and enter the Europa League after finishing third in their Champions League group.
Club Brugge - The Belgians are ranked one place below Celtic and like Leverkusen, arrive from the Champions League. They were runners-up in 1975/76.
Copenhagen - Celtic met the 42nd-ranked Danes in the Champions League group stages in 2004/05, winning one and losing one.
Eintracht Frankfurt - Germans finished behind Arsenal in Group F, and are ranked five places above Celtic. They won the tournament in its UEFA Cup days in 1979/80.
Getafe - The Spaniards are ranked in 79th place, but won four of their six group matches. Their tournament best is reaching the quarter-finals in 2007/08.
Ludogorets - Bulgarians are ranked 60th, and finished as runners-up to Espanyol in Group H. Previous best is the round of 16 in 2013/14.
Olympiacos - Celtic have played the 35th-ranked Greeks twice, with one draw and one defeat in the 1974/75 European Cup.
Roma - The Serie A giants could be lying in wait for Celtic. They finished second behind Istanbul Basaksehir in Group J, and their best result was as losing finalists in 1990/91.
Shakhtar Donetsk - The Hoops have faced the Ukrainian side twice in the UCL group stages, with two wins and two defeats against the current 19th-ranked team.
Sporting CP - Celtic first met the Portuguese side in 1983/84's UEFA Cup, and again in 1993/94, winning two and losing two.
Wolfsburg - The Bundesliga side finished runners-up to Gent in Group I, and have twice reached the quarter-finals, in 2009/10 and 2014/15. They are ranked 52nd.
Wolves - A potential brand new opponents for Celtic, the English side finished runners-up behind Braga in Group K.
WHO RANGERS COULD FACE
Ajax - Last season's semi-finallists have dropped into the Europa League after finishing third in their Champions League group. The Dutch side won the tournament in 1991/92.
Arsenal - Battle of Britain, anyone? The two-time runners-up won Group F ahead of Eintracht Frankfurt and could face former Liverpool captain Steven Gerrard in the round of 32.
Basel - Young Boys' league rivals Basel are in the mix, having won Group C. They reached the semi-finals in 2012/13.
Benfica - The 20th-ranked Portuguese side drop into the UEL from the Champions League. Always the bridesmaid but never the bride, they've been runners-up three times.
Braga - 2010/11's runners-up topped Group K ahead of Wolves, scoring 15 goals and losing none of their games.
Espanyol - The Spaniards were beaten finallists in 2006/07, which was the last time they participated in the competition. The 78th-ranked side won Group H ahead of Ludogorets.
Gent - Gent reached the quarter-finals in 1991/92 but haven't bettered it since. Currently second in the Belgian league, Rangers could be drawn to face the Group I winners.
Inter Milan - Three-time winners Inter could lie in wait, and currently lead Serie A. They dropped into the Europa League after finishing third in the Champions League.
Istanbul Basaksehir - The Turks are ranked 93rd, but won Group J ahead of Roma so are no mugs. This year marks their best performance to date.
LASK Linz - The Austrian side are the lowest-ranked seeds, at 133, but they won Group D ahead of Sporting CP. They've never made it beyond the round of 32 however.
Malmo - The Swedes won Group B ahead of near-neighbours Copenhagen, and have reached the round of 32 in consecutive seasons.
Man United - The 2016/17 winners won Group L and are the second highest ranked seeds.
Salzburg - Ranked 27th, they were beaten finallists in 1993/94 and drop into the UEL from the Champions League.
Sevilla - The highest-ranked seeded team have won the trophy five times, including three on the trot between 2013 and 2016. They won Group A ahead of APOEL.