The Gunners are now sixth in the Premier League with little prospect of finishing in the top four and taking one of the Champions League qualification spots.
Arsene Wenger's side will play the first leg at home against Atletico, who are favourites to win the competition for the third time.
They did prevail 6-3 on aggregate, but not before being given a scare.More news: Supreme Court to hear plea on allocation of sensitive cases
On the other side of the draw to Arsenal and Atletico, Marseille will have their sights set on a final outing on French soil.
Ultimately, the victor of this season's Europa League will qualify for next season's UEFA Champions League.
They have a strong recent record against English opposition in knockout ties, however, winning their last three and have a formidable attack featuring Diego Costa and Fernando Torres.
Madrid declined to put a timescale on Costa's return from a problem that saw him substituted in the 1-0 defeat by Sporting Lisbon in the quarter-final second leg on Thursday.