Pep Guardiola faces his former club as Manchester City play six-time winners Bayern Munich.
Inter Milan face Benfica and Serie A champions AC Milan take on current leaders Napoli.
If Chelsea and Manchester City get through, they will meet in an all-Premier League semi-final while AC Milan or Napoli will face Inter Milan or Benfica in the other semi-final.
The first legs of the quarter-finals take place on 11-12 April, with the return games on 18-19 April.
The first legs of the semi-finals will be on 9-10 May, and the second legs on 16-17 May.
The Ataturk Olympic Stadium in Istanbul, Turkey, will host the final on 10 June.
Chelsea beat Real in the semi-finals on their way to winning the trophy in 2020-21 before losing 5-4 on aggregate to the Spanish giants last season in the quarter-finals.
Manchester City and Bayern Munich have not met competitively since 2014 when Guardiola was in charge of the German club.
Inter Milan v Benfica
Manchester City v Bayern Munich
AC Milan v Napoli
Champions League semi-final draw
AC Milan or Napoli v Benfica or Inter Milan
‘Fiercely tough routes’ – analysis
Graham Potter’s Chelsea have improved recently but they will be firm underdogs against holders Real Madrid, who disposed of Liverpool with ease in the last 16. Real are led by former Chelsea boss Carlo Ancelotti, the only manager to win the tournament four times.
Manchester City, seeking their first Champions League crown, will be favourites against Bayern Munich but the Bundesliga champions have such a rich history in the tournament and proved their pedigree by knocking out Paris St-Germain. They can never be underestimated.
Bayern also have fit-again former Liverpool striker Sadio Mane, who was a constant thorn in the side of City and manager Pep Guardiola during a stellar career at Anfield, which included a Champions League win and two losses in the final.
With the last-four draw also made, there is now the possibility of an all-English semi-final should Chelsea and City progress.
But for now both Potter and Guardiola know they must navigate a way past two giants of the Champions League who will be filled with belief that they can overcome the Premier League clubs.