Chelsea will play holders Paris St-Germain in the Champions League round of 16 while Manchester City will face Real Madrid in the knockout stages for a fifth straight season.
Although six Premier League clubs have qualified for the last 16 there will be no all-English ties, with leaders Arsenal to face Bayer Leverkusen.
Newcastle United will meet Barcelona, Liverpool take on Galatasaray and Tottenham have been drawn against Atletico Madrid.
The first legs will be played on 10 and 11 March, with the second legs to take place on 17 and 18 March.
Newcastle are at home for their first leg with Barca, while their Premier League rivals are all away.
The final will be played at the Puskas Arena in Budapest, Hungary, on Saturday, 30 May.