Reigning champions Real Madrid will face Paris Saint-Germain in the Champions League round of 16, while Chelsea take on Barcelona.
Manchester United have a first ever competitive meeting with Sevilla, Manchester City play Basel and Liverpool are up against Porto, but fellow group winners Tottenham Hotspur have a tough test in Italian champions Juventus.
Bayern Munich, who finished second to PSG in Group B, play Besiktas and Shakhtar Donetsk take on Roma.
The biggest tie of the round, though, sees Madrid -- winners 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 pay the price for a slow start to the season that saw them unexpectedly finish runners-up to Tottenham in the group stage.
The Spanish champions' 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.
"We must trust in our players, who know how to play this type of game. Hopefully we arrive with a full squad, and have the fortune that you always need in this sort of tie. We will see how we arrive at the games.
"This is the biggest tie of the round. For the players who will be on the pitch, it will be the most entertaining of all."
Former PSG defender Maxwell, now an ambassador for the Ligue 1 club, said on UEFA's website: "It's a good draw, with two good games to play. Our fans will like it after we were knocked out by Barcelona last season. It will be nice. It's a beautiful challenge for the club. I think we're ready for that."
PSG president Nasser Al-Khelaifi added: "We have big respect for Real Madrid. It will be two great matches. The fans will have magic football moments away and at the Parc des Princes. As I always say, we need to be ready to play all the teams and we will be ready."
English champions Chelsea have also suffered for having to settle for second place in their group behind Roma, with a match-up with Ernesto Valverde's revitalised Barcelona representing a significant hurdle if they 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.
Guillermo Amor, Barca's director of institutional relations, said: "We knew there was a high chance we could get Chelsea and so it was. It's welcome. If you want to win the competition, you have to beat everyone.
"It's going to be a great knockout tie. We'll go into it with optimism, confidence and a huge desire to get through."
Valverde said: "It's a tough draw for us because of the magnitude of the opposition, but we knew it wasn't going to be easy because there were really good teams in the draw. Chelsea are champions of the Premier League, but we're excited about the tie, even though it will be difficult. It's a great tie to play in for us, and also for the fans. In that respect, it will be easy to motivate ourselves for the games.
"Chelsea are a strong and physical team, with a clear tactical system in place. They take advantage of the physical nature of the Premier League well. And with the signing of [Alvaro] Morata they've added pace in attack, while [Eden] Hazard is very good between the lines."
Among the other Premier League clubs, United, City and Liverpool will all be favourites to reach the quarterfinal stage after avoiding Madrid and Bayern, but Spurs must overcome a Juve side who -- despite a relatively disappointing campaign so far -- have reached two of the last three finals.
Juve boss Massimiliano Allegri tweeted: "Wembley awaits us, one of the sacred temples of this sport. Spurs are young and talented, but if we're #Juve we'll make it!"
Sevilla winger Nolito, who joined the Andalusian club this summer after one season at Manchester City, said he expects a tough game against United.
"I said it this morning when I got to the changing room that I dreamed last night that we got United, and now Jesus [Navas] reminded me of that," Nolito said in Marca.
"I will return to Manchester and I hope it will be a happy occasion, taking a good result there, but it's a very complicated tie. Any rival in the Champions League last 16 is going to be challenging and we've got one of the toughest ones.
"United is a great team, with world-class players who need no introduction, and it's [Old Trafford] a great stage. We will try to compete against them and go through."
Sevilla sporting director Oscar Arias says Celta Vigo's performance against United last season in the Europa League semifinals gives them hope.
Celta, who were coached by current Sevilla boss Eduardo Berizzo, lost 2-1 on aggregate but made life difficult for Jose Mourinho's side.
"We're going to have chances," Arias told beIN Sports. "We know it's going to be very difficult. It's a powerful rival and it's a very strong team.
"Last season Celta came close to eliminating them. We hope to have the opportunity to progress."
Five-time European champions Bayern will be relieved to avoid the continent's biggest sides after coming in second, but forward Thomas Muller warned that the Turkish champions will pose a substantial threat.
"I watched Besiktas' recent games against Leipzig [in the group stage]," Muller said. "They certainly unsettled Leipzig a little, especially in the first match in front of their imposing home fans. So we have to expect that and our alarm bells will have to be switched on for the away leg.
"Of course, we are the better team on paper, but you have to play two games first. Naturally, we are not displeased with the draw and are looking forward to the last 16."
Shakhtar will host Roma in their adopted home city of Kharkiv, with their stadium in Donetsk having been ruled unsafe for games since conflict flared in 2014 between government forces and pro-Russian separatists in eastern Ukraine.
"It's very, very difficult," said Shakhtar CEO Sergiy Palkin, whose team edged Napoli to advance. "It's a very, very big effort for our club."
Ties to be played Feb. 13, 14, 20 and 21 and March 5, 6, 12, 13
Juventus vs. Tottenham Hotspur
Basel vs. Manchester City
Porto vs. Liverpool
Sevilla vs. Manchester United
Real Madrid vs. Paris Saint-Germain
Shakhtar Donetsk vs. Roma
Chelsea vs. Barcelona
Bayern Munich vs. Besiktas