Changes in mean-square charge radius δ〈r2〉, and magnetic dipole moments μ1 have been measured for a series of neutron-deficient gold isotopes between A = 186 and 196, and for neutronrich 198,199Au, using the PILIS system on-line with the ISOCELE mass separator. These measurements confirm the existence of the shape transition between A = 186 and 187. The measured μ1 values have been compared with calculations using Nilsson, and symmetric-rotor-plus-quasiparticle models. The results are consistent with the interpretation that 186Au is prolate, and that the heavier isotopes have oblate, or possibly triaxial deformation.