The men from Dens Park raced to the semi-finals before succumbing to eventual winners AC Milan.
He negotiated his release after refusing a pay cut along with several other high earners at Dens Park.
BBC: SPORT | Football | My Club | Dundee Utd | Wilkie signs Dundee United deal
The game will be played at Dens Park, with proceeds being split in half between the Tayside clubs.
McDonald kept Dundee's promotion hopes alive after scoring an injury-time winner against Partick Thistle at Dens Park on Saturday.
Their first match in charge of Dundee will be Tuesday's league game against former club Queens at Dens Park.
Dion McLeish was arrested at Dens Park stadium on Wednesday night after widespread disturbances in the Bob Shankly stand.
Rangers followed last week's hammering of Dundee at Dens Park with a disappointing performance in front of their own fans.
Scott was relieved of his duties at a board meeting at Dens Park, 15 months after taking charge for a third time.
Meanwhile, Dundee have been forced to postpone Monday's fundraising derby match with Dundee United because of the wintry conditions around Dens Park.
Eventually they also hope to buy Dens Park back from current owner John Bennett, who is an associate director at rivals Dundee United.
Ebbe Skovdahl's Aberdeen produced a fantastic second-half display to defeat Dundee at Dens Park, and climb off the bottom of the Scottish Premier.
Brannan, who is set to stand down as chairman has admitted to having invested several hundred thousand pounds in the Dens Park club.
The Trust will comprise business people who are sympathetic to the Dens Park club and hopes to raise enough to bring Dundee out of administration.
The First Division leaders parted company with Jocky Scott on Saturday, 15 months after he returned to Dens Park for his third spell at the club.
The pair leave First Division rivals Queen of the South to take over at Dens Park, with the league leaders three points clear in the promotion race.
It was with Dundee that Khizanishvili first came to prominence in British football, earning himself a move to Scottish giants Rangers after just 51 appearances at Dens Park.
Melville has been trying to negotiate a deal to bring Dens Park back under Dundee's ownership, with the stadium currently owned by John Bennett, who is about to rejoin the board at rivals United.
The Dens Park club were subsequently served with a 25-point penalty by the Scottish Football League, which is currently under appeal, and have also been banned from signing any new players until they exit administration.
The wily Argentine, who scored twice in the 2-2 draw between the sides at Dens Park earlier this month, had a free role behind strikers Steve Lovell and Mark Burchill and was a constant threat with his sharp twists and turns.
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