Celtic and Rangers will meet in the Scottish Cup semi-final at Hampden, while holders Hibernian face Aberdeen in the other last four match.
The draw was made at Hampden on Sunday evening following Aberdeen's 1-0 quarter-final win over Partick Thistle at Pittodrie.
Celtic sealed their spot by coming from behind to beat St Mirren 4-1 earlier in the day.
The semi-final ties will be played on April 22/23.
Aberdeen manager Derek McInnes expects a tough match against Neil Lennon's Hibs, but admitted to a slight sense of relief over the draw.
"If we are all being honest, Celtic are the strongest team by a long way," he told BBC Radio Scotland.
"So it is a good draw and Hibs will probably see it as a good draw.
"Hibs have done really well and are holders and this is the type of game you want to be involved in.
"If you look at the level of player Hibs have got, the experience of the manager and the fact they won the cup last year and have that experience, there shouldn't be too much between the teams.
"If we are deemed to be favourites, so be it and we just have to do our business on the pitch."
Celtic and Rangers meet in the league on Sunday, with Brendan Rodgers' team having won the three matches between the sides so far this season.
Hibs beat Rangers 3-2 in last season's final to lift the Scottish Cup for the first time in 114 years.
They have played Aberdeen 32 times in the Scottish Cup, winning nine times, losing 13 times with 10 matches ending in draws.