The Blues paid around £500,000 to pluck the highly-rated teenager from Ibrox once he turned 16, and he made his senior debut for Frank Lampard's side earlier this season.
But FIFA have hit Rangers with a fine of £7,800 as part of their wider crackdown on transfers involving youth players.
Chelsea were hit with a transfer ban for their own involvement in youth transfers and are appealing the decisions, but the Light Blues have now been caught up in the controversy.
FIFA found that Rangers entered into a third-party arrangement by agreeing not to sell Gilmour to any other clubs before his 16th birthday.
World football's governing body said: "The committee has no doubt that these clauses entitled [Chelsea] to influence on the policies of Rangers and Ajax, since it could prevent them from loaning the player to another club.
“In this respect, the committee considers that clubs, in order to be considered truly independent, shall be free to negotiate and loan their players with no need to obtain the authorisation from another club."
FIFA claims the agreement "limited the independence of the respective clubs, since they had the obligation, upon request of Chelsea, to release the players in question so that they could attend take part to specific trainings and matches" with the Stamford Bridge outfit.