Defending Champions Real Madrid will face French giants Paris Saint-Germain (PSG) while Barcelona draw against Premier League champions Chelsea in the round of 16.
Premier League leaders Manchester City will play Switzerland's Basel, Manchester United face La Liga side Sevilla and Liverpool take on Portugal's Porto.
A record five English teams progressed from the group stage this season.
Real Madrid, who are aiming for a 13th title and third in a row, were handed a tough draw against big-spending PSG after finishing behind Tottenham in Group H.
The group winners will be away in the round of 16 first legs on 13/14 and 20/21 February, and at home in the return matches on 6/7 and 13/14 March.
The final will take place in Kiev on 26 May.
Here are the full draws:
Real Madrid v PSG
Chelsea v Barcelona
Bayern Munich v Besiktas
Basel v Manchester City
Porto v Liverpool
Sevilla v Manchester United
Juventus v Tottenham
Shakhtar Donetsk v Roma