CAS also said it had told FIFA to submit the GFA's application to its annual Congress which has the power to grant membership.
The tribunal added the Congress, which meets in Mexico City next week, "shall take all necessary measures to admit the Gibraltar Football Association as a full member of FIFA without delay".
FIFA said in a statement that its council would discuss the issue early next week and decide on a response "including a potential request to amend the 66th FIFA Congress agenda in order to submit the Gibraltar FA's application".
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Gibraltar became a member of UEFA in 2013 after a 14-year struggle during which it faced opposition from Spain.
The British territory was twice rebuffed by European football's ruling body and took its case to CAS which ruled in its favour.
UEFA then said Gibraltar's teams would be kept apart from Spain in any competition in which they took part.
Gibraltar's national team made their competitive debut in the 2016 European Championship qualifying campaign. They lost all 10 matches, conceding 56 goals.
Overall, they have played 18 matches, including friendlies, managed one win against Liechtenstein, and have employed three coaches.
Angel Maria Villar, president of the Spanish football federation, refused to comment when approached by reporters at his hotel in Budapest where UEFA is holding its annual Congress on Tuesday.
(Writing by Brian Homewood in Budapest; Editing by Louise Ireland and Tony Jimenez)
