1650s, "lasting four years;" as "happening once every four years," 1701; from quadri- + ending from biennial, etc. Correct formation would be quadriennial (compare Latin quadriennium "period of four years"). As a noun from 1640s. Related: Quadrennially.
quadrant
quadraphonic
quadrat
quadratic
quadratus
quadrennial
quadri-
quadricentennial
quadricep
quadriceps
quadrifid