The Gunners drew 2-2 at home with the Catalan giants in last season's quarter-finals before crashing 4-1 in the return leg.
Spurs topped their group ahead of Inter Milan after a thrilling 4-3 defeat in Italy and a win at White Hart Lane.
First-leg ties will be played on the 15/16 and 22/23 of February with the second legs scheduled for 8/9 and 15/16 March.
Roma v Shakhtar Donetsk
Lyon v Real Madrid
Marseille v Manchester United
Copenhagen v Chelsea