When the 17-year-old first move to the Stamford Bridge club in July, the two clubs were not able to agree on the fee.
Exeter will receive at least half the fee as a guarantee. The rest of the fee will depend on whether Ampadu becomes a regular at the club.
There is also a clause in the agreement that will give Exeter a 20 percent sell-on fee. If Chelsea were to cash in on the player, the club would be in for a windfall.
A Professional Football Compensation Committee statement read: "Chelsea Football Club should pay Exeter City an initial net fee of £850,000. In addition to the initial payment a fee of £450,000 is also payable.
"This fee incorporates an amount for the player signing a first professional contract, making five first-team appearances and obtaining a senior international cap."
The Exeter chairman Julian Tagg was not happy with the ruling.
He told the club's official website: "Whilst the club recognise, that the compensation fee is not a transfer fee, but instead to reward the club for its investment in the training and development of a proven outstanding player, and that the tribunal has awarded Exeter significant contingent sums, to say that we are disappointed is an understatement.
"We are disappointed for our fans, our academy, which works so hard on producing talented young players like Ethan and for our management and coaching team who bring these players into the first team and beyond as part of supporting the work of the FA in its objective to produce international players of the highest quality which we believe we have done.
"However, above all, we are disappointed for football as we feel this decision sends the wrong message in terms of financial reward for those owners, chairmen, managers and coaches up and down the country who are also working as hard as us to improve their clubs by producing talented home-grown players for both club and country."