Madrid will play Ajax, who finished second in their group behind Bayern Munich, and Barcelona face a Lyon side that are currently 13 points behind Ligue 1 powerhouses Paris Saint-Germain.
Meanwhile, Premier League leaders Liverpool have been handed a Champions League last-16 tie against German giants Bayern Munich.
In the first fixture drawn in Nyon on Monday morning, Premier League champions Manchester City were paired against German club Schalke.
Manchester United were handed a tough tie against French champions Paris Saint-Germain.
Tottenham Hotspur, who qualified as runners-up in their group behind Barcelona, will also face Bundesliga opposition as they face Borussia Dortmund.
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