Manchester United has a first ever competitive meeting with Sevilla, Manchester City plays Basel and Liverpool is up against Porto, but fellow group winner Tottenham Hotspur has a tough test in Italian champion Juventus.
Bayern Munich, which finished second to PSG in Group B, plays Besiktas and Shakhtar Donetsk takes on Roma.
The biggest tie of the round, though, sees Madrid – winner in both 2016 and 2017 – facing a PSG side widely considered among the leading contenders to win the trophy this season after bringing in Neymar, Kylian Mbappe and Dani Alves in the summer.
Madrid pays the price for a slow start to the season that saw them unexpectedly finish runner-up to Tottenham in the group stage.
The Spanish champion’s director of institutional relations, Emilio Butragueno, told beIN Sports: "It could have been the final, for the power of the two clubs, but that happens in a draw – luck plays a role.
"We will meet them in the last 16, which is a bit early, we could say. Logically we are both challengers for the trophy."
The two clubs were paired in the group stage two seasons ago, when Rafa Benitez's Madrid were outplayed for spells in both games but drew 0-0 away and won 1-0 at home.
"Each summer they have bought enormous players and are getting stronger all the time," Butragueno added. "They had almost perfect group stage. They have great power up front with Neymar and Mbappe."
English champion Chelsea has also suffered for having to settle for second place in its group behind Roma, with a matchup with Ernesto Valverde's revitalized Barcelona representing a significant hurdle if the Blues are to progress.
Chelsea and Barca have developed a rivalry in the Roman Abramovich era, with Andres Iniesta settling a bitter semifinal contest with a last-minute winner in 2009, while the Blues won out in the last four 2012 en route to their only success in the competition.
Among the other Premier League clubs, United, City and Liverpool will all be favorites to reach the quarterfinal stage after avoiding Madrid and Bayern, but Spurs must overcome a Juve side which – despite a relatively disappointing campaign so far – has reached two of the last three finals.
UEFA Champions League round of 16 draw:
Juventus (ITA) vs. Tottenham Hotspur (ENG): February 13 – March 7
Basel (SUI) v Manchester City (ENG): February 13 – March 7
Porto (POR) v Liverpool (ENG): February 14 – March 6
Real Madrid (ESP) v Paris (FRA): February 14 – March 6
Chelsea (ENG) v Barcelona (ESP): February 20 – March 14
Bayern München (GER) v Beşiktaş (TUR): February 20 – March 14
Sevilla (ESP) v Manchester United (ENG): February 21 – March 13
Shakhtar Donetsk (UKR) v Roma (ITA): February 21 – March 13