Aberdeen were paired with St Johnstone in the other semi-final when the draw was conducted by former Scotland manager Craig Levein and SPFL Secretary Iain Blair at Hampden on Thursday.
The ties will be played on the weekend of February 1 and 2 with the venues to be confirmed.
Hearts defeated Edinburgh rivals Hibernian 1-0 at Easter Road on Wednesday night to book their place in the last four and their reward is a rematch with Inverness, who they beat 5-4 on penalties last January before losing to St Mirren in the Hampden final.
Caley Thistle overcame Dundee United in the quarter-finals with a 2-1 extra-time success on Tuesday night.
Aberdeen reached the semi-finals by beating Motherwell 2-0 on Wednesday despite having Joe Shaughnessy sent off.
St Johnstone clinched their spot by seeing off Championship side Morton thanks to Gary McDonald's controversial injury-time winner.
And Aberdeen boss Derek McInnes is looking forward to taking on Saints, whom he managed for almost four years until leaving in October 2011.
Looking ahead to the semi-finals, the 42-year-old said: "St Johnstone is a club I know both as a player and manager.
"Watching them recently I can see they are going from strength-to-strength and when the game comes around it will be tough.
"And it was always going to be tough whoever we got, so we are delighted just to be in the draw.
"It's always a big moment playing a former club but a semi-final is a big occasion in itself and I hope we're in good form.
"But if we don't win it, then I would be pleased for St Johnstone to win."
The Dons lasted lifted silverware in 1995 but McInnes is not getting ahead of himself.
The Pittodrie club are currently second in the SPFL table and, with Celtic already knocked out , McInnes prefers to play down his club's chances.
He added: "We are now 90 minutes away from the final and with the squad we've got I feel we can do well this season but to do that we need to strive for consistency."
He is also taking a low key approach with regards to Aberdeen's chances of catching Celtic in the league - the Hoops are currently six points clear at the top.
McInnes went on: "That's a long way away. And I'm saying that without wanting to sound like we lack ambition.
"We are in good form but a long way off where we want to be."
Aberdeen v St Johnstone
Hearts v Inverness
Ties to be played weekend of February 1 and 2