Hearts’ match with Hibs is a re-run of the semi-final two seasons ago, and leaves open the possibility of a 2020 re-run where Celtic defeated the Jambos on penalties.
The Old Firm semi-final is the first at this stage of the competition since 2017 when Celtic won through, though the sides have met at the National Stadium since – Celtic taking the Betfred Cup in 2019.
The Glasgow rivals also met in the last 16 of last year’s competition where Rangers won 2-0 at Ibrox.
However, it is the first time in the competition’s history that the final four has comprised of the big two from Glasgow and Edinburgh and Still Game actor and comedian Greg Hemphill made the historic draw, setting up the ties, live on broadcaster Premier Sports.
Celtic had earlier sealed their place with a 3-0 win over Dundee United at Tannadice on Monday, a day after Rangers ensured their progression with a win over Dundee just along the street.
Hearts and Hibs took their places with wins over St Mirren and Motherwell respectively.
Both matches are scheduled to be played at the National Stadium Hampden Park on the weekend of April 16 & 17. The final is then more than a month later on May 21.
Reigning holders St Johnstone relinquished their grip on the trophy with an exit to League Two leaders Kelty Hearts in January.