"showy, tastelessly rich," c. 1600; earlier "joyfully festive" (1580s), probably a re-adjectivizing of gaudy (n.) "large, ornamental bead in a rosary" (early 14c.) via the noun gaud + -y (2.). In early Modern English it also could mean "full of trickery" (1520s).
Or possibly the adjective is from or influenced by Middle English noun gaudegrene (early 14c.), name of a yellowish-green color or pigment, originally of dye obtained from the weld plant (see weld (n.1)). This Germanic plant-name became gaude in Old French, and thus the Middle English word. Under this theory, the sense shifted from "weld-dye" to "bright ornamentation."
As a noun, "feast, festival" 1650s, from gaudy day "day of rejoicing" (1560s).
-ness
word-forming element denoting action, quality, or state, attached to an adjective or past participle to form an abstract noun, from Old English -nes(s), from Proto-Germanic *in-assu- (cognates: Old Saxon -nissi, Middle Dutch -nisse, Dutch -nis, Old High German -nissa, German -nis, Gothic -inassus), from *-in-, originally belonging to the noun stem, + *-assu-, abstract noun suffix, probably from the same root as Latin -tudo (see -tude).