FIFA also added two member associations to its ranks on Friday: Kosovo and Gibraltar.
They become the 210th and 211th members of the football family and can start their preparations for the 2018 World Cup qualifying tournament.
The huge majorities they received for their inclusion -- 86 percent and 93 percent respectively -- represent huge victories for the pair, particularly given the strong opposition they have faced from more powerful neighbours.
Spain has strongly opposed Gibraltar's progress towards FIFA membership, forcing the British overseas territory to go to the Court of Arbitration for Sport to move the process along.
Kosovo's elevation to independent football nation status, meanwhile, has been fought all the way by Serbia.
Serbia refuses to recognize Kosovo's declaration of political independence in 2008 which is accepted by more than 100 United Nations member states.
At UEFA's congress in Budapest last week, Kosovo's bid for membership was only narrowly approved by 28 votes to 24, and the vice president of Serbia's FA spoke out against Kosovo's admission to FIFA from the floor in Mexico City.
But his calls were ignored, prompting an emotional Kosovo FA president Fadil Vokrri to say: "The players and people of Kosovo have been waiting for this for a long time -- thank you."
Kosovo's entry could see a wave of transfer requests to FIFA from players who opted to represent countries, including Albania and Switzerland, before Kosovo started to get international recognition just two years ago.
Those votes brought the business of FIFA's 66th annual congress to a close, leaving the stage to Infantino to send everybody home with smiles on their faces.
"The crisis is over," he said. "We can look forward to a bright future."
It is likely FIFA and UEFA will need to separate the Serbia and Kosovo national teams and clubs in competition draws. Similarly, Gibraltar and Spain teams have been kept apart since the British territory joined UEFA in 2013.
Information from Press Association and The Associated Press was used in this report.