Abby Musinguzi, alias Abitex, a popular club promoter known for staging major festivals, and the party's MC, Elvis Francis Juuko, were charged with 13 counts of rash and negligent acts leading to deaths and injury.
The deadly crush occurred at a shopping mall in the capital Kampala as revelers thronged through a single exit to watch a midnight fireworks show.
Concert organizers had closed other exits to prevent revelers who had not paid from gaining access to the overcrowded venue inside the shopping mall.
Most of the victims were aged between 10 and 20, police said, and three remain in hospital with severe injuries.
"Musinguzi and Juuko will be reappearing in court on February 7 this year for the hearing (of the case)," their lawyer Erias Lukwago told AFP.
Juuko was arrested on Friday in Mityana, 60 kilometres (37 miles) west of Kampala after going on the run after the tragedy.
A third person arrested and charged, the owner of the Freedom City mall, did not appear in court on Tuesday after being freed from police custody.
Juuko is accused of encouraging partygoers to go through a narrow passage from the concert hall to watch the fireworks, triggering the stampede.
The magistrate's court granted each of the accused cash bail of two million Ugandan shillings ($540).
The court was packed with survivors and relatives of the victims, as well as families of the two men charged, politicians, and lawyers.
President Yoweri Museveni ordered a speedy investigation into the crush and offered the families of the deceased money to help with funeral expenses.