We consider the production of $W\gamma$ and $Z\gamma$ pairs at hadron colliders. We report on the complete fully differential computation of radiative corrections at next-to-next-to-leading order (NNLO) in QCD perturbation theory. The calculation includes the leptonic decay of the vector boson with the corresponding spin correlations, off shell effects and final-state photon radiation. We present numerical results for $pp$ collisions at 7 and 8 TeV and we compare them with available LHC data. In the case of $Z\gamma$ production, the impact of NNLO corrections is generally moderate, ranging from 8% to 18%, depending on the applied cuts. In the case of $W\gamma$ production, the NNLO effects are more important, and range from 19% to 26%, thereby improving the agreement of the theoretical predictions with the data. As expected, the impact of QCD radiative corrections is significantly reduced when a jet veto is applied.