Ange Postecoglou's men eased past Jablonec 7-2 on aggregate to reach the playoff round, while AZ qualified for this stage courtesy of their third-placed finish in the 2020-21 Eredivisie season.
After a testing few weeks in which hardly anything could go right for Postecoglou, the new Celtic boss has seen his fortunes dramatically improve over the past few weeks, with the Bhoys heading into Wednesday's first leg on a four-game winning streak in all tournaments.
After Midtjylland crushed their Champions League dreams early doors, Celtic dusted themselves down for a Europa League third-round tie with Jablonec, and Postecoglou's men marched to a 4-2 victory in the Czech Republic before a 3-0 success on home soil.
A 6-0 thrashing of Dundee in Scottish Premiership action was sandwiched in between those ties, and Celtic also advanced to the quarter-finals of the Scottish League Cup over the weekend with a thrilling 3-2 success over Hearts as Odsonne Edouard, Kyogo Furuhashi and Stephen Welsh made the net ripple.
With a dismal start to his competitive reign firmly consigned to history, Postecoglou has his sights firmly set on a fifth consecutive Europa League group-stage appearance for Celtic, who last suffered defeat at this stage of Europe's secondary tournament all the way back in 2011.
Having held down third spot in the Eredivisie table for the final months of the 2020-21 season, AZ Alkmaar missed out on Champions League qualification by a whisker and are now vying for a third consecutive group-stage appearance in the Europa League.
Pascal Jansen's side enjoyed a solid pre-season campaign with victories over OFI, Real Sociedad and Torino, but their Eredivisie season kicked off in disappointing fashion on Saturday, as RKC Waalwijk frontman Michiel Kramer struck the only goal of the game for his side on the stroke of half time.
If a lack of competitive action was one thing, kicking off the 2021-22 season scoreless, pointless and winless is hardly a recipe for success either, but AZ can take solace in the fact that they have never been knocked out at this stage of the Europa League when they have progressed this far previously.
Both clubs do have the safety net of the Europa Conference League should they fail to produce the goods over the next week, and Wednesday's game marks the first-ever meeting between the two sides in competitive action, with AZ's only other clash against Scottish opposition seeing them claim a 1-0 win over Rangers in the 2004-05 UEFA Cup.
Celtic are sweating over the fitness of Ryan Christie after the midfielder picked up a knock in training, and Postecoglou has admitted that he is "not sure" if the in-form Scotsman will be passed fit for the first leg.
However, the Bhoys coach does expect Liel Abada to return to the squad after the new arrival missed out against Jablonec and Hearts as a precautionary measure, but Christopher Jullien will still be out for "a little while" according to Postecoglou.
Joe Hart has made the number one spot his own since arriving from Tottenham Hotspur earlier in the summer, and the Premier League winner should form part of an untouched backline for the hosts.
Meanwhile, AZ left-back Owen Wijndal is still nursing a groin problem and is not expected to be passed fit for the first leg, with Thijs Oosting - a number 10 by trade - forced to deputise in defence at the weekend.
Highly-rated attacking duo Myron Boadu and Calvin Stengs have both completed moves to Ligue 1 with Monaco and Nice respectively, while Teun Koopmeiners found himself among the substitutes at the weekend amid talk of an imminent exit.
Jansen must surely consider starting the 23-year-old in a game of this magnitude, though, while Maxim Gullit - the son of Ruud - is another option at left-back in Wijndal's absence, and attacker Jesper Karlsson will miss out due to suspension.
Celtic possible starting lineup:
Hart; Ralston, Starfelt, Welsh, Taylor; McGregor, Turnbull, Rogic; Abada, Edouard, Furuhashi
AZ Alkmaar possible starting lineup:
Verhulst; Sugawara, Martins Indi, Chatzidiakos, Gullit; Koopmeiners, Clasie, De Wit; Gudmundsson, Pavlidis, Aboukhlal
We say: Celtic 2-0 AZ Alkmaar
It would be folly to write off the side who finished third in the Eredivisie last term, but AZ are in a rut with top players already gone and others being strongly linked with exits.
In contrast, Celtic finally appear to have found their groove under Postecoglou, and we can only back the Bhoys to claim a healthy first-leg advantage this week.