The first draw had paired Lionel Messi's PSG with Cristiano Ronaldo's Manchester United, instead the former Barcelona star renews his rivalry with the La Liga leaders, who will also welcome back former captain Sergio Ramos.
Messi scored 26 times against Real in all competitions when he was at Barcelona.
The match will also give Real Madrid a close-up look at French forward Kylian Mbappe who they attempted to prise from PSG in the close season.
Manchester United instead take on Atletico Madrid, who had originally been drawn with Bayern Munich.
The Spanish champions had tweeted they had asked Uefa for 'explanations and solution after the mistakes made' in the first draw.
Ninety minutes after the first draw began UEFA said they would redo it.
In the re-draw Liverpool take on Inter Milan and Bayern Munich meet RB Salzburg- the first Austrian side to qualify for the knockout stages. The only pairing to feature in both draws pitted Chelsea against Lille.
Confusion had begun when United were erroneously drawn against Villarreal - a side they had already been paired with in Group F.
UEFA deputy general secretary Giorgio Marchetti apologised for the "technical issue our draw is experiencing" before asking former Arsenal forward Andrey Arshavin to try again, and this time it was neighbours Manchester City who were paired with the Yellow Submarine.
When Atletico Madrid were the next side to be drawn, Marchetti said: "For Atletico Madrid, the possibility are all [teams] except for Liverpool, who was in the same group, and Manchester United as they were already drawn."
But as United's drawing was a mistake, they should still have been potential opponents for Atletico.
Real Madrid were reported to have asked for the draw to re-start when the errors was made, which would have left them with Benfica. Instead it was completely redone.
LAST-16 DRAW
Bayern Munich v RB Salzburg
Manchester City v Sporting Lisbon
Ajax Amsterdam v Benfica
Lille v Chelsea
Manchester United v Atletico Madrid
Juventus v Villarreal
Liverpool v Inter Milan
Real Madrid v Paris St Germain
Seeded teams (named first) will play the second leg at home. The first legs are scheduled to take place on Feb. 15-16 and Feb. 22-23 while the second legs will be played on March 8-9 and March 15-16.
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