Holders St Johnstone will play Celtic in the League Cup semi-final, with Rangers and Hibs meeting to fight for a place in the final.
The draw was made after Thursday’s quarter-final ties completed the line-up for the last four in the competition.
Jota, Liel Abada and David Turnbull all scored as Celtic beat Raith Rovers 3-0 at Parkhead to book their place in the draw.
Ange Postecoglou’s first trip to the national stadium will see him take on the St Johnstone side that won both domestic cup competitions against the odds last season.
First half goals from Joe Newell, Scott Allan and Martin Boyle were enough to see off Dundee United, despite Peter Pawlett clawing a goal back for the hosts after the break. Jack Ross’s side will now meet Rangers, who beat Livingston on Wednesday to progress.
The semi-finals will be played on the weekend of November 20/21.