Celtic will face Danish Superliga runners-up Midtjylland in the Champions League second qualifying round.
Ange Postecoglou's first test will come at home, with the first leg on 20/21 July and the return the following week.
In the Conference League, Aberdeen will face Hacken of Sweden and Hibernian will play Mons Calpe of Gibraltar or Andorra's Santa Coloma.
Both will be at home in the second qualifying round on July 22, with the return leg a week later.
Should Celtic progress, they would still have two rounds before reaching the group stage.
Defeat would mean a place in the Europa League third qualifying round against either Anorthosis Famagusta of Cyprus or the Czech Republic's Jablonec.
What about the other British sides?
Elsewhere in the Champions League, Northern Ireland's Linfield could face Ferencvaros of Hungary if they get past Zalgiris Vilnius of Lithuania in the first qualifying round.
And Welsh counterparts Connah's Quay Nomads will face Teuta of Albania or Sheriff Tiraspol of Moldova should they defeat Alashkert of Armenia.
Meanwhile, the winners of the Europa Conference League first-round tie between Dundalk or Newtown will face Levadia Tallinn of Estonia or St Joseph's of Gibraltar.
The winner of the all-UK tie between Glentoran and The New Saints will take on Europa of Gibraltar or Kauno Zalgiris of Lithuania, while Bala Town lie in wait should Larne beat Aarhus of Denmark.
Rosenborg of Norway await should Sligo Rovers defeat Iceland's Hafnarfjordur, while AEK Athens will be Coleraine's opponents should they beat Velez of Bosnia-Herzegovina.
What do we know about Midtjylland?
Midtjylland navigated their way past Ludogorets Razgrad, Young Boys and Slavia Prague - who knocked Rangers out of the Europa League - to reach last season's group stage for the first time.
However, they lost to the Ibrox club in the Europa League third qualifying round in the previous campaign.
They finished two points behind Brondby in the Danish top flight last term and are captained by former Celtic defender Erik Sviatchenko.
Celtic went into Wednesday's draw as one of the seeded sides in a section of clubs who finished runners-up in their respective leagues and drew the Danes instead of Turkey's Galatasaray and Austria's Rapid Vienna.
What about Hacken?
The Gothenburg-based side finished third in the Allsvenskan last season but currently sit bottom of the table with only six points from eight games in the 2021 campaign.
They have lost in the second qualifying round of the Europa League in the last three seasons, against Cork City, RB Leipzig, then AZ Alkmaar.
But they have won their one previous meeting with a Scottish side - edging out Dunfermline Athletic 2-1 on aggregate in the Uefa Cup in 2007.
And Hibs' potential opponents?
Mons Calpe, established in 2013, are making their debut in European competition after finishing fourth in the Gibraltar Premier Division's top-six championship play-off.
Santa Coloma, who were second in the Primera Division play-off, have only won two of their 22 European ties - both Champions League qualifiers - beating Urartu of Armenia in 2014, then Tre Penne of San Marino in 2019.
The sides meet on 8 July and 15 July to decide who will face Jack Ross' men.