It originates from the French word of the same spelling.
Some linguists argue that the word is an onomatopœia, simply imitating the sound it describes; others present different theories on its origin. Walther von Wartburg, a German linguist, suggested that the word was based on the Hebrew greeting barukh habba, an equivalent of 'welcome' meaning “blessed be the one who comes”.
John Peter Maher, another linguist who has studied the roots of the word, believes the word could have originated in Colloseum rings, from the Italian word bravo.
Another theory is origin from the Aretin (Italian dialect) word "barruccaba", meaning "confusion".
Greek scholar James Updegraff and his colleagues (Roy Perkins, Chris Eggemeyer, and Rory Soltan) suggest that the word may come from the Greek word βρυΧα, the second person singular form of the word meaning 'to roar'.
Pop Culture Reference: Firesign Theater quote: "What's all this Brouhaha? Brouhaha? Ha ha ha!"