Premiership winners Rangers will face Malmo or HJK Helsinki in the Champions League third qualifying round.
And Celtic will play PSV Eindhoven or Galatasaray if they beat Midtjylland in the second qualifying round.
Ange Postecoglou's side meet the Danes in Tuesday's first leg in Glasgow and travel for the second leg on 28 July.
And the loser of the PSV Eindhoven v Galatasaray tie will face Scottish Cup winners St Johnstone in the Europa League third qualifying round.
Celtic, who have confirmed Callum McGregor as their new club captain, will face Czech side Jablonec in the Europa League third qualifying round if they lose to Midtjylland.
Swedes Malmo or Finland's HJK will host Steven Gerrard's Rangers on 3 or 4 August, with the return at Ibrox on 10 August.
Those would be the same dates for Celtic in the third qualifying round, with Dutch side PSV or Turkey's Galatasaray away in the second leg. The Europa League third qualifying round dates are 5 August (first leg) and 12 August (second leg).
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Sides that win at the Champions League third qualifying round stage progress to the play-off round, which will be played over 17/18 and 24/25 August. The draw for the play-off round is 2 August.
Losing sides at the third qualifying round stage drop into the Europa League play-off round (19 and 26 August).
Rangers have reached the last 16 of the Europa League for the past two seasons while Celtic were knocked out at the group stage of last season's competition after a last-32 appearance the previous year.
Scotland have not had a representative in the group stage of the Champions League since Brendan Rodgers' side featured there in season 2017-2018, with Rangers last making the group stage under Walter Smith in 2010-11.
However, the following season Malmo knocked Ally McCoist's Rangers out at the qualifying stage. The Ibrox side have no previous competitive meetings with HJK but did sign prolific scorer Alfredo Morelos from the Finnish side in 2017.
St Johnstone, who also won last season's League Cup, return to European competition for the first time in four years.