Scottish champions Rangers have been drawn to play Malmo or HJK Helsinki in the Champions League third qualifying round, while Celtic will face PSV or Galatasaray if they beat Midtjylland in the second qualifying round.
Rangers' fixtures with Malmo or HJK Helsinki will be their first in the Champions League since 2011, while they have not reached the group stage since 2010.
Celtic are bidding to reach the group stage for the first time in four years, but they must first beat Denmark's Midtjylland in their two-legged second qualifying round tie before taking on PSV or Galatasaray.
- Scottish Premiership home kits for 2021/22
- Ange Postecoglou: Celtic working hard on more signings
- Scans find heart issue for Rangers' Nnamdi Ofoborh
The first leg of that tie will take place at Celtic Park on Tuesday night, and will be Ange Postecoglou's first competitive game as Celtic manager.
Both Rangers and Celtic will be away in their first legs of the third qualifying round, which will be played on August 3 or 4. The second legs will take place on August 10.
Should HJK Helsinki beat Malmo in their second qualifying round encounter, it will set up a reunion for Rangers striker Alfredo Morelos, who played for the Finnish club for just under 18 months before moving to Ibrox in the summer of 2017.
As last season's Scottish Premiership winners, Rangers will be playing in the champions' path section of the draw, while Celtic, who finished second to Rangers, will be competing in the league path.
Sides on the champions' path that are beaten in the third qualifying round will enter the Europa League play-offs. If they lose at that stage, they will compete in the inaugural Europa Conference League.
However, the sides on the league path that are knocked out in the third qualifying round will automatically enter the group stages of the Europa League.
As a result, both Rangers and Celtic are guaranteed to be playing group-stage European football this season.
In the Europa League draw, St Johnstone will play the losers of the PSV-Galatasaray Champions League clash in the third qualifying round.
Celtic will play Czech side Jablonec in that competition if they cannot get past Midtjylland.
In the Europa Conference League, Hibernian will take on Maltese side Gzira United or Rijeka of Croatia in the second qualifying round if they get past Santa Coloma.
Aberdeen will take on Austria Vienna or Icelandic side Breidablik if they beat BK Hacken.
Ajer, Ntcham left out of Celtic's CL squad
Kristoffer Ajer and Olivier Ntcham have been left out of Celtic's squad ahead of their Champions League second qualifying round fixtures against Midtjylland.
Defender Ajer is unfit and has also been linked with a move to Brentford, while Ntcham's future is unclear after he spent the second half of last season on loan at Marseille.
Speaking after Saturday's friendly defeat to Preston, Postecoglou said: "I'm concentrating on the ones who are involved. I can't afford to waste time on anyone other than the ones who are here and committed to being here."
New signing Osaze Urhoghide has been included in the squad, but there is no place for fellow recent arrivals Liel Abada and Kyogo Furuhashi.
Celtic can add two more players to the squad before midnight on Monday. The game takes place at Celtic Park at 7:45pm on Tuesday.