FIFA has already said that both teams will be able to take part in the 2018 World Cup qualifying competition which starts in September.
Kosovo, which joined European football's governing body UEFA last week, was elected despite strong opposition from Serbia.
It was not immediately clear whether Kosovar players who have already played for another national team would be allowed to switch nationalities.
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FIFA rules do not allow players to change allegiance but there have been calls to make an exception for Kosovo, which could have a big impact on Switzerland and Albania who both have contingents of players with Kosovar roots.
FIFA rejected an application from the British territory of Gibraltar in 2014 but the Court of Arbitration for Sport (CAS) last week ordered it to reconsider and accept the request.
Gibraltar has been a member of UEFA since 2013 which itself followed a 14-year battle during which they took their case to CAS.
"Rare are the occasions when Gibraltar stands up and addresses the entire world," Gibraltar FA president Michael Llamas said. "It's been a very long road towards FIFA membership for us and it feels fantastic today."
Gibraltar made their competitive debut in the 2016 European Championship qualifying campaign, where they lost all 10 matches, conceding 56 goals.
Overall, they have played 18 matches, including friendlies, under three coaches and have achieved just one win, against Liechtenstein.
(Editing by Tony Jimenez and Ian Chadband)
