We have investigated the atomic structure of the Au/GaAs(111)B surface and have performed scanning tunnelling microscopy (STM) simulations of the surface by using first-principles calculations. The atomic geometry determined with Au adatoms located at every third threefold hollow hcp site of the Ga lattice, agrees well with results reported from STM and low-energy electron diffraction experiments. The simulated STM images support experimental observations of bright centers with triangular spots. The calculated value of the diffusion barrier height of the Au adatom quantitatively explains the experimentally observed reconstruction of the wetting layer of Au on the Au/GaAs(111)B surface.