Premier League champions Manchester City will play six-time winners Bayern Munich.
Inter Milan face Benfica and AC Milan play fellow Italian side Napoli.
The two-leg quarter-finals take place on Tuesday 11 and Wednesday, 12 April, with the return games on 18-19 April.
More to follow.
Champions League quarter-final draw
Real Madrid v Chelsea
Inter Milan v Benfica
Manchester City v Bayern Munich
AC Milan v Napoli