New emission branching fraction measurements for 836 lines of the first spectrum of vanadium (VI) are determined from hollow cathode lamp spectra recorded with the National Solar Observatory 1m Fourier transform spectrometer (FTS) and a high-resolution echelle spectrometer. The branching fractions are combined with recently published radiative lifetimes from laser-induced fluorescence measurements to determine accurate absolute atomic transition probabilities for the 836 lines. The FTS data are also used to extract new hyperfine structure A coefficients for 26 levels of neutral vanadium. These new laboratory data are applied to determine the V abundance in the Sun and metal-poor star HD 84937, yielding log{epsilon}(V)=3.956+/-0.004 ({sigma}=0.037) based on 93 VI lines and log{epsilon}(V)=1.89+/-0.03 ({sigma}=0.07) based on nine VI lines, respectively, using the Holweger-Muller 1D model. These new VI abundance values for the Sun and HD 84937 agree well with our earlier determinations based upon VII.