1630s, "an overflowing," from French exubérance (16c.), from Late Latin exuberantia "superabundance," abstract noun from exuberare "be abundant, grow luxuriously" (see exuberant). Usually figurative in English, especially of joy, happiness, etc. Exuberancy attested from 1610s.

"state or quality of being rampant, exuberance, extravagance," 1660s, from rampant + abstract noun suffix -cy.

1775, "of or pertaining to the writings or style of 16c. French author François Rabelais," whose writings "are distinguished by exuberance of imagination and language combined with extravagance and coarseness of humor and satire." [OED]