Manchester United will play AC Milan at home in the first leg of their last-16 Europa League tie.
Arsenal, finalists in 2019, travel to Greek side Olympiakos, who knocked them out of the competition in the last 32 last year.
Tottenham will travel to Croatian side Dinamo Zagreb while Rangers have been drawn against Czech side Slavia Prague, who defeated Leicester City this week.
The eight last-16 ties will be played on 11 and 18 March.
Full last 16 draw:
Ajax v BSC Young Boys
Dynamo Kiev v Villarreal
AS Roma v Shakhtar Donetsk
Olympiakos v Arsenal
Dinamo Zagreb v Tottenham
Manchester United v AC Milan
Slavia Prague v Rangers
Granada v Molde