We present internal surface brightness profiles, based on Hubble Space Telescope/ACS imaging in the F606W bandpass, for 131 globular cluster (GC) candidates with luminosities L = 104-3 × 106 Lo in the giant elliptical galaxy NGC 5128. Several structural models are fitted to the profile of each cluster and combined with mass-to-light ratios (M/L values) from population-synthesis models, to derive a catalogue of fundamental structural and dynamical parameters parallel in form to the catalogues recently produced by McLaughlin & van der Marel and by Barmby et al. for GCs and massive young star clusters in Local Group galaxies. As part of this, we provide corrected and extended parameter estimates for another 18 clusters in NGC 5128, which we observed previously. We show that, like GCs in the Milky Way and some of its satellites, the majority of globulars in NGC 5128 are well fitted by isotropic Wilson models, which have intrinsically more distended envelope structures than the standard King lowered isothermal spheres. We use our models to predict internal velocity dispersions for every cluster in our sample. These predictions agree well in general with the observed dispersions in a small number of clusters for which spectroscopic data are available. In a subsequent paper, we use these results to investigate scaling relations for GCs in NGC 5128.