Rangers have been drawn to play Olympiakos or Ludogorets in the Champions League play-offs should they beat Swedish champions Malmo in the third qualifying round, while Celtic will face AZ Alkmaar in the Europa League play-offs if they beat Jablonec.
Steven Gerrard's side found out in Monday's draw they will play the Greek Super League or Bulgarian First League winners in order to reach the Champions League group stages.
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The first-leg ties for the play-offs are on August 17/18, with the return legs on August 24/25.
Rangers travel to Malmo for the first leg of their third qualifying round tie on Tuesday at 6pm, before the return clash at Ibrox on Tuesday, August 10 at 8pm.
As last season's Scottish Premiership winners, Rangers will be playing in the champions' path section of the draw.
Sides on the champions' path that are beaten in the third qualifying round will enter the Europa League play-offs. Rangers will face FC Kairat Almaty or Alashkert FC there if they lose to Malmo.
If they lose at that stage, they will compete in the inaugural Europa Conference League.
Celtic hope to reach Europa League after Midtjylland CL defeat
Meanwhile, Ange Postecoglou will hope his side can bounce back after they were knocked out of the Champions League qualifiers by Midtjylland last week.
Postecoglou saw his side give up a lead again as they slumped to a 2-1 defeat after extra-time in Denmark to lose 3-2 on aggregate and miss out on the group stages for a fourth consecutive year.
That defeat meant Celtic will travel to the Czech Republic to take on Jablonec in the Europa League third qualifying round on Thursday, and will face AZ Alkmaar in the play-offs if they win.
AZ Alkmaar finished third in the Eredivisie last year behind Ajax and PSV Eindhoven.
The first legs of the EL play-off ties take place on August 19, and the second on August 26.
St Johnstone face tough path to Europa League
In the Europa League draw, St Johnstone also found out they were drawn against Danish side Randers in the play-offs.
However, they must first get past Galatasaray, who finished second in the Turkish Super Lig last season. They were knocked out in the second qualifying round of the Champions League by PSV.
Callum Davidson's side begin their European campaign this Thursday away at Galatasaray, kick-off at 7pm.
Gerrard: CL a target since day one
Gerrard says qualifying for the Champions League group stage has been a target since the day he arrived at Rangers but insists his players cannot afford to underestimate a dangerous Malmo side.
Rangers' previous appearance in the group stage of the competition was during the 2010/11 season as they finished third in Group C behind Manchester United and Valencia.
"It's something that's been a target since day one, but we always knew it was going to be a process and a patient one," Gerrard said on Monday.
"The first challenge was always to get European football back from a Europa League point of view and the challenge here was to always finish top of the league at some point. We managed to do that in spectacular form last year and that's given us the opportunity to qualify.
"There's still a lot of work to do and some big challenges ahead - Malmo first and foremost who we've got a lot of respect for.
"They've got big quality in the team as well as a really strong mentality in terms of the group.
"I don't think they're a team full of egos, they all work extremely hard for each other and in the right areas of the team they've got big quality.
"We'll have to be right at it over two legs to get the opportunity to get into the play-off first and foremost, so getting into the Champions League's not really the focus right now, it's trying to get into that play-off round."