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This Text and Tune is often credited to Henry Carey, 1740, although there is controversy with many votes, including the British monarchy's, for anonymous. On official occasions, only the first verse is usually sung, and occasionally verse 3. The tune has been used by many countries for anthems and hymns.
According to the French encyclopaedia, Quid, the music is by Giam Battista Lulli (Jean-Baptiste Lully in the French form). It was loosely based on a hymn sung when the (French) king arrived at an event, Domine Salvum Fac Regem. When Louis XIV was scheduled to open the educational institution at St-Cyr (1686), his mistress (later, queen), the Marquise de Maintenon, commissioned Lully to write the tune to be sung by the pupils as Dieu Protège le Roi. The French, apparently, did not use it again until 1745 at which time the Old Pretender, claiming to be King James III of England, was organising his rebellion from France (he lived at St-Germain-de-Laye). Madame de Maintenon presented him with the words and music as his National Anthem. (It is not clear who wrote the English words but the implication is that Mme de Maintenon either wrote them herself or commissioned them.) The song was sung for the first time in Britain when Bonnie Prince Charlie landed in Scotland. There are apparently some legal testaments to this story. first publicly performed in London, 1745
From:http://ingeb.org/songs/godsaveo.html