It will be the latest in a series of high-profile encounters between Wasps and Leicester, which last season featured two epic European Cup battles - both won by Tigers - and the Premiership final when Wasps gained revenge and retained their league title at Twickenham.
Leicester booked their place in the Cardiff double-header by defeating Northampton on Saturday, while Wasps overpowered Saracens on Sunday.
Bath, meanwhile, topped their qualifying pool courtesy of victories over Bristol, the Ospreys and Gloucester, and Llanelli won a group that featured Sale Sharks, Newcastle and Leeds.
"It is great to have got to the semi-final and to have the opportunity of playing at the Millennium Stadium," said Wasps rugby director McGeechan.
"It will be a new experience for a lot of our players to play there.
"The draw has given us a big game against Leicester, and after last season's titanic battles in the European Cup, the scene is now set for the two clubs to meet again in the Powergen."
Leicester, despite considerable success in the European Cup and English Premiership, have not tasted domestic cup success since Martin Johnson captained Tigers to a 9-3 victory over Sale in 1997.
"It will be a big test, a great spectacle for our fans and a great day out at the Millennium Stadium," said Leicester coach Pat Howard.
"Now we know we have got Wasps again, I am sure the players will be looking forward to the game even more."
England head coach Andy Robinson will have more reason than most to keep an eye on events at the Millennium Stadium.
Up to 12 of his 22-man match-day squad involved during the titanic contest against New Zealand last month, could be involved on March 4, with the semi-finals scheduled just eight days before England tackle Six Nations title favourites France in Paris.
Llanelli, meanwhile, are determined to keep the Welsh flag flying, despite a powerful three-pronged English attack, and reach an April 9 Twickenham showdown with Wasps or Leicester.
"There are four quality teams and there were never going to be any easy draws," said Scarlets skipper Simon Easterby.
"But I am pleased we have avoided Wasps. We will have already played them twice in the European Cup by March, and we would probably know each other too well.
"Bath are the cup kings of England, up against the cup kings of Wales, so that should make for a great game, and being back in the Millennium Stadium is certainly something for us to look forward to."
Bath's England hooker Lee Mears added: "It will be a fantastic experience.
"We are two matches away from some silverware, and that is a huge motivating factor, as is the fact we are playing in a terrific venue, and, of course, there is a European Cup place at stake."