And the fixture at Ibrox on Saturday week will have a total of six officials.
Madden's assistants for the game between the League One champions and the Premiership club will be Graham Chambers and Alastair Mather.
The fourth official will be Calum Murray while the additional assistant referees will be John Beaton and Alan Muir.
United have sold 10,500 tickets for the semi-final against Rangers.
United had previously indicated they would seek up to 20,000 tickets for the encounter.
United director Derek Robertson said: "We'll probably have to get back to the SFA in the next couple of days to let them know the numbers. I would urge anyone who has not yet bought their tickets to do so in the next few days."
With Hampden Park being redeveloped for the Commonwealth Games, the SFA chose Rangers' stadium to host both semi-finals back in October.
Robertson said it would be the biggest support the club had taken to a semi-final.
He added: "We're very happy with the numbers so far."
United were initially offered 11,063 seats for the match.
But the club's representative said that "in order to ensure maximum attendance" United would prefer to only be allocated the 8012-seat Broomloan Road stand.
The club had complained about Ibrox being chosen as the venue for the tie.
But last weekend SFA chief executive Stewart Regan defended the move.
"It was a planning decision," Regan said. "When you're putting a major cup competition together, you spend a lot of time discussing it with your sponsors.
"We certainly did that with William Hill.
"We needed to take the semi-finals and final to venues that would cope with the demand for tickets."