Manchester United were drawn against Belgian side Club Brugge in the Europa League round of 32, while Arsenal will meet Olympiakos.
United, who won the competition in 2017, finished top of their group and were top seeds for the draw, as were last season's runners-up -- which means both sides will play the first tie away from home.
United met Brugge in the 2015-16 Champions League preliminaries when Memphis Depay and Wayne Rooney inspired them a 7-1 aggregate victory.
Arsenal and Olympiakos have met eight times in the Champions League, with four victories apiece. In their last match in 2015, Olivier Giroud's hat trick in Athens gave Arsenal the three-goal victory required to progress from their group.