The last time the two Scottish capital clubs met in the last eight of the competition in Leith was back in November 2006 when a goal from Rob Jones sent the Hibees en route towards Hampden glory 5-1 over Kilmarnock.
Scottish Championship strugglers Morton, shock Parkhead conquerors of favourites Celtic in the last round, host St Johnstone at Cappielow.
Dundee United, with on-loan Scotland forward David Goodwillie netting a hat-trick in an eye-catching 4-1 win over Scottish Premiership rivals Partick Thistle, must travel to league leaders Inverness Caledonian Thistle.
Motherwell host Aberdeen at Fir Park in a third all-Premiership last-eight tie.
Tuesday, Oct 29 (1945):
Inverness v Dundee Utd
Wednesday, Oct 30:
Hibernian v Hearts (1900)
Morton v St Johnstone (1930)
Motherwell v Aberdeen (1945)