Chelsea have been drawn against Barcelona in the last 16 of the Champions League, while Tottenham will face Italian champions Juventus.
Premier League leaders Manchester City will play Switzerland's Basel, Manchester United face La Liga side Sevilla and Liverpool take on Portugal's Porto.
Holders Real Madrid will face Paris St-Germain.
A record five English teams progressed from the group stage this season.
Chelsea were the only English team to make it through as runners-up, with the other four sides all topping their respective groups.
Juventus v Tottenham
Basel v Manchester City
Porto v Liverpool
Sevilla v Manchester United
Real Madrid v PSG
Shakhtar Donetsk v Roma
Chelsea v Barcelona
Bayern Munich v Besiktas
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