  We present measurements of the baryon acoustic peak at redshifts z = 0.44,
0.6 and 0.73 in the galaxy correlation function of the final dataset of the
WiggleZ Dark Energy Survey. We combine our correlation function with
lower-redshift measurements from the 6-degree Field Galaxy Survey and Sloan
Digital Sky Survey, producing a stacked survey correlation function in which
the statistical significance of the detection of the baryon acoustic peak is
4.9-sigma relative to a zero-baryon model with no peak. We fit cosmological
models to this combined baryon acoustic oscillation (BAO) dataset comprising
six distance-redshift data points, and compare the results to similar fits to
the latest compilation of supernovae (SNe) and Cosmic Microwave Background
(CMB) data. The BAO and SNe datasets produce consistent measurements of the
equation-of-state w of dark energy, when separately combined with the CMB,
providing a powerful check for systematic errors in either of these distance
probes. Combining all datasets we determine w = -1.03 +/- 0.08 for a flat
Universe, consistent with a cosmological constant model. Assuming dark energy
is a cosmological constant and varying the spatial curvature, we find Omega_k =
-0.004 +/- 0.006.
