Arsenal have been drawn against current holders Bayern Munich.
Chelsea, the 2012 winners,face Galatasaray and Manchester United will meet Greek side Olympiakos.
Phil McNultyChief football writer
“The Champions League draw is the perfect illustration of the perils of finishing second in your group as the reward for Manchester City and Arsenal is a last-16 meeting with Barcelona and holders Bayern Munich.
“Manchester United and Chelsea fulfilled their part of that bargain and will feel confident of winning. Manchester City’s sheer attacking firepower will give them real hope against Barcelona – with the Spanish media already making it clear they would have preferred to avoid a trip to Etihad Stadium.
“As for Arsenal, they at least have memories of a Champions League win against Bayern in the Allianz. Manager Arsene Wenger will know the scale of their task but they have already won away at last season’s runners-up Borussia Dortmund in this season’s competition.”
Elsewhere, AC Milan face Atletico Madrid, Bayer Leverkusen meet Paris St-Germain, Schalke face Real Madrid and Zenit St Petersburg will meet last year’s runners-up Borussia Dortmund.
Chelsea and Manchester United have the advantage of playing the second leg at home after winning their groups, while City and Arsenal will have to travel away for the second legs of their ties.
City beat Bayern Munich 3-2 in their final Group D game and could have topped their group had they won 4-2.
Their manager Manuel Pellegrini said: “I think Barcelona will be very concerned that they have drawn us. They are not the team of two years ago.”
City’s chief executive officer Ferran Soriano and director of football Txiki Begiristainused to work at Barcelona, who sold Yaya Toure to Cityin 2010.
Begiristain told his club’s official website:”I think it will be a great match. Ours is a team with a lot of confidence especially after winning against the champions in Munich – that will give us a lot of confidence.
“Our manager knows perfectly Barcelona because he managed in Spain for a long time. In this sense, we are confident.
“If you want to win the Champions League you have to beat the biggest teams, Barcelona are one of the biggest teams.”
Previous meetings between Arsenal and Bayern Munich
5 Dec 2000 -Arsenal 2-2 Bayern
14 Mar 2001 -Bayern 1-0 Arsenal
22 Feb 2005 -Bayern 3-1 Arsenal
9 Mar 2005 -Arsenal 1-0 Bayern
19 Feb 2013 -Arsenal 1-3 Bayern
13 Mar 2013 -Bayern 0-2 Arsenal
Arsenal won 2-0 at Bayern Munichin March but went out on away goals in last season’s quarter-finals following a 3-1 defeat in the first leg, with the Germans going on to beat Dortmund in the final.
Bayern have also knocked the Gunners out of the tournament on their two previous meetings.
Bayern captain Philipp Lahm said: “It’s a prestigious tie but a tough opponent. It was the hardest draw amongst the second-placed teams. Arsenal are certainly not a team you’d hope to face.”
Chelsea will face Didier Drogba for the first time since the Ivorian striker left Stamford Bridge after eight yearsin 2012.
Blues manager Jose Mourinho claimed last weekthat a meeting with Drogba and Galatasaray was the draw he wanted.
Manchester United, who finished top of their group, have won each of their four previous meetings with Olympiakos.
Champions League round of 16 draw:
Manchester City v Barcelona – 18 February
Bayer Leverkusen v Paris St-Germain – 18 February
Arsenal v Bayern Munich – 19 February
AC Milan v Atletico Madrid – 19 February
Olympiakos v Manchester United – 25 February
Zenit St Petersburg v Borussia Dortmund – 25 February
Galatasaray v Chelsea -26 February
Schalke v Real Madrid – 26 February
Atletico Madrid v AC Milan – 11 March
Bayern Munich v Arsenal – 11 March
Barcelona v Manchester City – 12 March
Paris St-Germain v Bayer Leverkusen – 12 March
Chelsea v Galatasaray – 18 March
Real Madrid v Schalke – 18 March
Borussia Dortmund v Zenit St Petersburg – 19 March
Manchester United v Olympiakos – 19 March