We derive peculiar velocities for the 6dF Galaxy Survey (6dFGS) and describe the velocity field of the nearby (z < 0.055) Southern hemisphere. The survey comprises 8885 galaxies for which we have previously reported Fundamental Plane data. We obtain peculiar velocity probability distributions for the redshift-space positions of each of these galaxies using a Bayesian approach. Accounting for selection bias, we find that the logarithmic distance uncertainty is 0.11 dex, corresponding to 26 per cent in linear distance. We use adaptive kernel smoothing to map the observed 6dFGS velocity field out to cz ~ 16000 km s-1, and compare this to the predicted velocity fields from the PSCz Survey and the 2MASS Redshift Survey. We find a better fit to the PSCz prediction, although the reduced χ2 for the whole sample is approximately unity for both comparisons. This means that, within the observational uncertainties due to redshift-independent distance errors, observed galaxy velocities and those predicted by the linear approximation from the density field agree. However, we find peculiar velocities that are systematically more positive than model predictions in the direction of the Shapley and Vela superclusters, and systematically more negative than model predictions in the direction of the Pisces-Cetus Supercluster, suggesting contributions from volumes not covered by the models.