This will be the first meeting between the sides in over six decades, and Celtic will look for a repeat of their two 1-0 wins over Slovan in the Cup Winners' Cup back in the 1960s.
Match preview
Like most Scottish clubs in recent times, apart from Rangers' run to the Europa League final in 2022, Celtic have seriously struggled to compete in Europe, especially in the Champions League.
Their last five qualifications for the group stage all ended in immediate elimination, and they have not progressed past the last 16 since a quarter-final defeat to Real Madrid in 1980.
Starting poorly has been the big issue, as remarkably, Celtic have never won the opening game of a Champions League campaign, drawing two and losing 10.
Having won all five of their league games so far without conceding this season though, Brendan Rodgers's side should come into this winnable encounter with plenty of confidence.
Some could claim that in the new format, Celtic's eight opponents are about as kind as they could have been drawn with, including their fixture on matchday one against competition debutants Slovan.
The Scottish champions will also face arguably the two weakest pot one sides in RB Leipzig and Borussia Dortmund, and they have gotten Club Brugge at home from pot two.
Pot three saw them presented with more clubs from minor leagues in the form of Young Boys and Dinamo Zagreb, but they will have to go to Villa Park after being drawn with Aston Villa from pot four.
Their Slovakian visitors will be looking to make sure they are not perceived as any sort of pushovers in their first-ever Champions League match in the competition proper here though.
Slovan have become just the fourth Slovakian club to qualify - the first since Zilina 14 years ago - and the target will be to become the first team from the country to make it past this stage.
What makes their qualification even more special was the fact they had to go through all four rounds of qualifiers, beating Struga Trim & Lum, Celje, APOEL Nicosia and Midtjylland to make it this far.
The Conference League had been Slovan's best friend, as they qualified for that competition in all three of its iterations so far before this season, and those escapades may well have given them more knowhow and experience of competing post-summer in Europe.
While Vladimir Weiss's side have certainly been handed one of the most difficult draws, it does give their supporters a few dream ties to look forward to, including this away trip to the atmospheric Celtic Park.
Visits to Bayern Munich and Atletico Madrid also await, while Manchester City and AC Milan will visit the Slovakian capital during the league phase.
This game could be highlighted as one of their best chances to pick up points, but Slovan have lost their last five matches against British clubs, and they are winless in nine since a victory over Derby County in 1975.
Weiss's men sit top of the Slovak top flight after a 2-1 win over Dunajska Streda at the weekend, making amends for a shock 5-0 home defeat to Zilina shortly after they secured qualification for the league phase.
Celtic form (all competitions):
W
W
W
W
W
W
Slovan Bratislava Champions League form:
W
W
W
D
D
W
Slovan Bratislava form (all competitions):
W
D
W
W
L
W
Team News
Maik Nawrocki is the only current Celtic player dealing with an injury at present, as a calf problem means he is unlikely to make the squad for this one.
New signing Arne Engels made an instant impact on his full debut, scoring in Saturday's 2-0 win over Hearts, and he could keep Paulo Bernardo out of the team here.
Also on the scoresheet at the weekend was another deadline day signing in Luke McCowan, but the former Dundee captain is expected to remain on the bench here.
Rodgers has been reluctant to make many changes recently given that their schedule has not been too congested, so Auston Trusty is still yet to make his debut either, but that could change in the coming weeks.
Slovan will be without central defender Lukas Pauschek after he sustained a shoulder injury on the opening day of the league season last month.
Goalkeeper Dominik Takac has only featured once in the league, but since signing from Spartak Trnava midway through the summer, he has played in all six of Slovan's subsequent European ties.
The man the home side will need to watch out for is Armenian Tigran Barseghyan, who has already contributed to 10 goals this season, including scoring six in six league games.
British fans watching on will recognise Kevin Wimmer after his brief spell at Tottenham Hotspur, where he played one Champions League group game, and is the only player with any experience in the side at this level.
At 37 years of age, Juraj Kucka may finally make his Champions League bow too, after failing to reach the competition during his spells at AC Milan and Trabzonspor.
Celtic possible starting lineup:
Schmeichel; Johnston, Carter-Vickers, Scales, Taylor: Engels, McGregor, Hatate; Kuhn, Kyogo, Maeda
Slovan Bratislava possible starting lineup:
Takac; Blackman, Kashia, Bajric, Wimmer; Szoke, Kucka, Tolic; Barseghyan, Strelec, Weiss Jr
We say: Celtic 2-2 Slovan Bratislava
Both sides have players in offensive areas capable of winning them the game in what could be an open, entertaining encounter.