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 \pm 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 \pm 0.006 .