Named Together Stronger, the lyrics written by Nicky Wire include the line "when (forward) Gareth Bale plays we can beat any side, with (defender) Ashley Williams we can win any fight".
Manics frontman James Dean Bradfield said the song was written for other tournaments only to be shelved when Wales invariably failed to qualify.
"It had always been on the cards," he told Wales Online.
"Nick had written lyrics for a song during previous campaigns but of course they'd all bitten the dust."
Wales, with Real Madrid's Bale as their talisman, have qualified for their first major tournament since the 1958 World Cup.
"We all watched qualification with so much trepidation which turned into expectation which eventually turned into joy," Bradfield said.
Wales have been drawn in Group B alongside England, Russia and Slovakia at next month's Euro 2016 finals in France.
(Reporting by Martyn Herman; Editing by Tony Jimenez)
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