Bolton have been drawn against Spanish high-flyers Atletico Madrid in the last 32 of the Uefa Cup.
Aberdeen, in the knockout stages of a European competition for the first time since 1986, will come up against 1996 winners Bayern Munich.
After winning their qualification group Everton take on Norwegian side SK Brann and Tottenham face Slavia Prague.
Rangers, who were eliminated from the Champions League, play Panathinaikos for a place in the last 16.
Aberdeen, Bolton and Rangers all play their first legs at home, while Everton and Tottenham have home advantage in the second.
Should Bolton overcome the Spaniards, who sit third in La Liga after spending heavily over the summer, they would take on either Sporting Lisbon or Basle in a bid to reach the quarter-finals.
The club's chief executive Allan Duckworth admitted Gary Megson's side face a huge task.
"It's a big one but they all are at this stage so we are pleased to be going to Spain.
"It's a formidable challenge but one that Gary Megson will relish so we are looking forward to that."
Progress for Aberdeen would pair them with the winners of the tie between Anderlecht and Bordeaux and Rangers would face Werder Bremen or Braga.
Rangers boss Walter Smith believes his side's Greek opponents will provide a stiff challenge.
"It's a difficult one in the sense that going away to any of the Greek teams is always going to be difficult," he said.
"There's always a very hostile atmosphere in the matches.
"We've already seen that when they came to Aberdeen to play. So it'll be a tough enough draw."
Last year was very disappointing to come out in the quarter-final and this year we want to go as far as possible
Damien Comolli, Tottenham's sporting director
Aberdeen, now managed by Jimmy Calderwood, beat Bayern en route to their 1983 Cup Winners' Cup triumph.
"It's a reward for a fantastic achievement by Jimmy and the players," said Aberdeen's captain from that night Willie Miller.
"If we can repeat something along the same lines then we can go into the game with confidence, but we are not kidding ourselves - Bayern are a top, top club."
Everton will be confident of setting up a last 16 clash with Rosenborg or Fiorentina and likewise Tottenham, who would play PSV Eindhoven or Helsingborg.
Everton secretary David Harrison said: "It's quite a short trip for us but we are looking forward to it.
"We put in some good performances in the group stages and hope it continues."
Tottenham's sporting director Damien Comolli refused to write-off Slavia, who Spurs beat in last year's first round and Arsenal thumped 7-0 in this season's Champions League.
"They have done well in the Champions League, beating Steaua (Bucharest) and drawing with Arsenal at home," Comolli told BBC Radio Five Live.
"We played them last year and know how difficult it was, we won there and at home but it was a tough game, especially over there.
"They have a mix of young players, who have been very successful on the international stage at under-17s, 19s and 21s, along with experienced players."
Last season Tottenham were knocked out by Juande Ramos's back-to-back winners Sevilla in the quarter-finals.
But with Ramos now in charge at White Hart Lane Comolli is hoping the Spaniard can repeat his feat.
"Last year was very disappointing to come out in the quarter-final and this year we want to go as far as possible, we are very ambitious.
"We are very happy with Ramos. We know his experience and success in Europe so he will bring it to us."
Draw for the last 32:
Aberdeen v Bayern Munich
AEK Athens v Getafe
Bolton v Atletico Madrid
Zenit St Petersburg v Villarreal
Galatasaray v Bayer Leverkusen
Anderlecht v Bordeaux
SK Brannv Everton
FC Zurich v Hamburg
Rangers v Panathinaikos
PSV Eindhoven v Helsingborg
Slavia Prague v Tottenham
Rosenborg v Fiorentina
Sporting Lisbon v Basle
Werder Bremen v Braga
Benfica v Nuremburg
Marseille v Spartak Moscow
(Ties to be played on 13/14 February and 21 February)
Draw for the last 16:
Anderlecht/Bordeaux v Aberdeen/Bayern Munich
Rangers/Panathinaikos v Werder Bremen/Braga
Bolton/Atletico Madrid v Sporting Lisbon/Basle
Galatasaray/Leverkusen v FC Zurich/Hamburg
AEK Athens/Getafe v Benfica/Nuremburg
Rosenborg/Fiorentina v SK Brann/Everton
Slavia Prague/Tottenham v PSV Eindhoven/Helsingborg
Marseille/Spartak Moscow v Zenit St Petersburg/Villarreal
(Ties to be played on 6 March and 12/13 March)