Hearts and Hibs were both landed with home draws in the sixth round of the William Hill Scottish Cup.
Daniel Stendel's side will face Rangers at Tynecastle while Hibs will welcome Inverness Caledonian Thistle to Easter Road.
Ties will be played on the weekend of 29 February, 2020, with televised matches to be confirmed nearer the time.
Hearts secured passage to the sixth round of the cup following a 1-0 away victory to Falkirk. Sean Clare's second half penalty was the difference between the sides.
Hibs earned their place after a convincing 4-1 win against BSC Glasgow. Marc McNulty scored a hat-trick while Greg Docherty scored his first goal for the club.
The other two quarter final ties will see St Johnstone face Celtic and St Mirren or Motherwell take on Aberdeen or Kilmarnock.
