The Dons advanced to the quarter-finals with a 2-1 win at Ayr United, while St Johnstone staged a dramatic comeback to see off Hearts 3-2 at McDiarmid Park.
The teams were paired against each other in the quarter-final draw, and that match will be played on Thursday, September 22nd.
The BT Sport cameras will be at Pittodrie to broadcast the game live from 7pm.