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.
The Blues have arguably been handed the most difficult tie, and it comes days after boss Antonio Conte conceded that their Premier League title defence was over following their defeat by West Ham, which left them 14 points adrift of Manchester City.
Champions League last-16 draw
Juventus v Tottenham
Shakhtar Donetsk v Roma