The two teams were unable to agree a fee when the 17-year old moved to Stamford Bridge in July last summer and the matter will be decided on Wednesday, April 18.
Exeter are entitled to a compensation fee for the player, as he is a product of the club's academy and under the age of 24.
Exeter do not expect the outcome of the tribunal, and the fee owed, to be known until a few weeks after the hearing.
In 2016, Ampadu became the youngest ever player to represent the League Two side in competitive action at the age of 15 years, 10 months and 26 days.
Since joining Chelsea, Ampadu has gone on to make seven first-team appearances for Antonio Conte's side and has been capped twice for Wales at senior level.