It said that Mercedes was guilty of a breach of the regulations and would be reprimanded, and suspended from taking part in the young driver test at Silverstone.
Pirelli was also reprimanded.
The Tribunal panel of Edwin Glasgow, Christy Harris, Patrick Raedersdorf and Anthony Scott Andrews heard arguments that Mercedes and Pirelli had brought the sport into disrepute.
During closing speeches at the hearing in Paris, Mercedes' legal representative Paul Harris had suggested that if the team was found guilty, then a reprimand and ban from the young driver test would be appropriate.
He said: "[The young driver test] is a three-day test, and it is a car test over which teams have full control and teams know everything about the tyres and cars.
"If we are in this territory then it is open to the International Tribunal to impose exclusions from events that are under FIA jurisdiction, and the young driver test is that."
The costs of the Tribunal case will be split between Mercedes, Pirelli and the FIA.
This year's young driver test takes place on July 17-19. Mercedes reserves Sam Bird and Daniel Juncadella were likely to have run.