This year’s final is to be held at Benfica’s Estadio da Luz in Lisbon on Saturday, 24 May.
United overturned a 2-0 deficit against Olympiakos to book their spot in the last eight, while Chelsea saw off Galatasaray.
The Premier League champions beat the Greeks 3-0 in the second leg to provide some much-needed relief for manager David Moyes and his players.
Now they will play German leaders Bayern, who Moyes believes are favourites to retain their European title after defeating Arsenal 3-1 on aggregate.
“I was thrilled we were in the draw and that we are in the quarter-final of the Champions League,” said the Scot. via BBC Sport