Also in March's ties, seven-time champions Lyon meet final hosts Juventus, Arsenal take on fellow former champions Wolfsburg and last season's two beaten semi-finalists are paired in Bayern Munich and Paris Saint-Germain.
The semi-final draw has also been made, with a potential tie between Lyon and Paris among the possibilities.
The first leg of the quarter-finals will take place from March 22-23, 2022, and the second leg, March 30-31, 2022.
The eight teams emerged after qualifying from the competition's first-ever home-and-away group stage, played between October and December, with last season's runners-up Chelsea among the clubs missing out. The full schedule of the ties will be confirmed in due course.
The so-called away goals rule has been removed, so ties level after 180 minutes in the quarter-finals or semi-finals will go to extra time irrespective of the number of goals each team has scored home and away. If the teams still cannot be separated after the additional 30 minutes, then it goes to a penalty shoot-out.
The draw for the competition's semi-final also took place and will look as follows Real Madrid/Barcelona vs Arsenal/Wolfsburg; Juventus/Lyon vs Bayern/Paris.
Nyon, December 20
Holders Barcelona will face Real Madrid in the quarter-finals after the UEFA Women's Champions League draw set the road to May's decider in Turin on Monday.
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