Rangers will play either Swedish side Malmo or Faroe Islands champions Torshavn in the third qualifying round of the Champions League.
Malmo are in pole position to take on Ally McCoist's side after a 2-0 victory in the first leg, with a trip to Torshavn to come on Tuesday.
The two-legged tie will begin with a home match on 26/27 July, with the away leg taking place the following week.
Rangers would face a further play-off game to reach the group stages.
"I think it is a more that acceptable draw for us," McCoist told the Rangers website. "In terms of travelling and organisation it is far better than some of the other possibilities like Georgia for example.
"I fully expect Malmo to get through. It would be a major shock if they were knocked out. Of course they are in the middle of their season so that gives them a bit of an advantage.
"At the same time our lads know the importance of the tie and I feel that will be a huge factor.
"We might be a little rusty in terms of competitive games but I feel that if we play as we can we have the opportunity to qualify."
Under Walter Smith, the Ibrox club finished third in a group that included Bursaspor, Valencia and finalists Manchester United last season, before beating Sporting Lisbon in the Europa League round of 32, and eventually losing out to PSV Eindhoven in the last 16.
Welsh champions Bangor City will face either Croatia's Dinamo Zagreb or Neftci PFK of Azerbaijan if they can overturn a 3-0 deficit against HJK Helsinki, while Northern Ireland's Linfield, who drew their first leg with BATE Borisov 1-1, will play either Valletta of Malta or Lithuania's FK Ekranas if they can progress.
Uefa Champions League third qualifying round draw:
FK Mogren/Litex Lovech v Skonto FC/Wisla Krakow
Maccabi Haifa/FK Borac v NK Maribor/ F91 Dudelange
HJK Helsinki/Bangor City v Dinamo Zagreb/Neftci PFK
KS Skenderbeu/APOEL FC v Slovan Bratislava/Kostan
Copenhagen v Shamrock Rovers/FC Flora Tallin
Genk v FK Partizan/FK Skendija
Rosenborg BK/Breidablik v FC Pyunik/Viktoria Plzen
FC Zestafoni/Dacia Chisinau v SK Strurm Graz/Videoton
Valletta/FK Ekranas v Linfield FC/Bate Borisov
Rangers v Malmo FF/HB Torshavn
Standard Liege v FC Zurich
FC Twente v FC Vaslui
Benfica v Trabzonspor
Dynamo Kiev v Rubin Kazan
Odense BK v Panathinaikos