Hearts and Hibs will take on opposition from Glasgow in the William Hill Scottish Cup quarter-finals.
The Jambos travel to Firhill to take on Championship side Partick Thistle, while Hibs host holders Celtic at Easter Road.
In the other two last-eight ties, Aberdeen will take on the winners of the replay between Kilmarnock and Rangers, while a Championship side is guaranteed to be in the semi-finals as Dundee United will welcome either Ross County or Inverness to Tannadice.
The matches are due to be played on the weekend of March 2.
Full William Hill Scottish Cup quarter-final draw: Aberdeen v Kilmarnock or Rangers; Dundee United v Ross County or Inverness; Partick Thistle v Hearts; Hibs v Celtic.