Hampden will host the Scottish league Cup semi-final between Celtic and Ross County, while St Johnstone will play Hibernian in Edinburgh.
Hibs will make the short trip across the capital to Tynecastle to face the Perth side on Saturday, January 30.
Ross County face holders Celtic at Hampden 24 hours later, with both matches kicking off at 3pm.
The Scottish Professional Football League stressed the arrangements had been agreed by all four clubs.
Ronny Deila's side beat Dundee United in last season's final and advanced to this year's last four after a 2-1 win over Hearts at Tynecastle, while upcoming opponents County progressed after victory over Highland rivals Inverness.
Hibernian cruised into the latter stages of the competition with a 3-0 win over Dundee United, while St Johnstone beat Championship side Greenock Morton.