Newcastle have been drawn against Kazakh side Qarabag, while Jose Mourinho's Benfica and Real Madrid will once again face each other after a dramatic final league phase tie.
Goalkeeper Anatoliy Trubin scored a 98th-minute goal in a 4-2 win to lift Benfica and push Real down into the play-offs.
Reigning champions PSG were handed an all-French tie against Monaco and Inter Milan will face tricky Norwegian side Bodo/Glimt.
Juventus play Galatasaray, Atletico Madrid face Club Brugge, Borussia Dortmund are against Atalanta and Bayer Leverkusen have Olympiacos.
Champions League knockout play-off draw (number denotes seeding):
Monaco (21) v PSG (11)
Galatasaray (20) v Juventus (13)
Benfica (24) v Real Madrid (9)
Borussia Dortmund (17) v Atalanta (15)
Qarabag (22) v Newcastle (12)
Club Brugge (19) v Atletico Madrid (14)
Bodo/Glimt (23) v Inter Milan (10)
Olympiacos (18) v Bayer Leverkusen (16)
When are the knockout play-offs?
The first legs of the knockout play-offs will take place on February 17th and 18th, and the second legs will be on February 24th and 25th.
The eight winners of the knockout play-offs will progress to the round of 16, where they will be drawn against the sides which finished first to eighth in the league phase. Those sides in order of final rank are:
1. Arsenal, 2. Bayern Munich, 3. Liverpool, 4. Tottenham, 5. Barcelona, 6. Chelsea, 7. Sporting, 8. Manchester City.
The next draw, which is for the round of the 16 plus the remaining bracket, will take place on Friday, February 27th, after the second legs of the knockout play-offs. The round of 16 will begin on March 10th.