The draw at UEFA headquarters in Nyon also paired Germany's Werder Bremen with Italy's Sampdoria and English Premier League Tottenham Hotspur face Switzerland's Young Boys.
Former European champions Ajax Amsterdam, hoping to reach the Champions League group stage for the first time in five seasons, were handed a tough draw against Dynamo Kiev in the final qualifying round on Friday.
The draw at UEFA headquarters in Nyon also paired Germany's Werder Bremen with Italy's Sampdoria and English Premier League Tottenham Hotspur face Switzerland's Young Boys, who dumped Fenerbahce out of the competition on Wednesday.
Ajax, absent from the group stage since 2005-06, will travel to Ukraine for the first leg on Aug. 17 or 18.
Dynamo's attack is spearheaded by former AC Milan and Chelsea striker Andriy Shevchenko, the third highest-ever scorer in the competition with 58 goals.
The Ukrainians comfortably beat Gent 6-1 on aggregate in the third qualifying round while Ajax struggled past PAOK Salonika on away goals after a 4-4 aggregate draw.
Previous appearance
Sampdoria are hoping to qualify for the Champions League for the first time. The Serie A side reached the final of the former European Cup in its last season in 1991-92, where they lost to Barcelona in their only previous appearance in Europe's top club competition.
Neither Young Boys nor Tottenham have played in the group stage, Tottenham having last taken part in Europe's top club competition 48 years ago.
All three ties will be played in the non-champions half of the draw along with Braga v Sevilla and Zenit St Petersburg v Auxerre.
For the second season running, non-champion teams from the bigger European leagues have been kept apart from champion teams from the smaller leagues to ensure that some of the latter are represented in the group stage.
In the champions half, Sheriff Tiraspol, who last season were one round from becoming the first Moldovan team to reach the group stage, were drawn against FC Basel.
Czech champions Sparta Prague face Zilina, from neighbouring Slovakia, and Rosenborg meet FC Copenhagen in an all-Scandinavian tie between two sides with past group stage experience.
Serbian champions Partizan Belgrade face Anderlecht, twice winners of the old Cup Winners' Cup and once of the UEFA Cup.
The 10 winners will be joined by 22 teams who qualified directly for the group stage.
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