The First Division outfit stated on their website that they were satisfied with the figure agreed.
And Clyde added that they were happy that the matter did not need to go to a compensation tribunal.
Clyde expect to hear from Fifa within seven days about their claim from Millwall over striker Tom Brighton.
Brighton joined the English club last summer, the 23-year-old having spent a season at Broadwood following his release by Rangers.
The 20-year-old Bryson has yet to make his debut for Killie, having picked up an injury early in the season.