We developed a spatially explicit model of a bioinvasion and used an approximate Bayesian computation (ABC) framework to make various inferences from a combination of genetic (microsatellite genotypes), historical (first observation dates) and geographical (spatial coordinates of introduction and sampled sites) information. Our method aims to discriminate between alternative introduction scenarios and to estimate posterior densities of demographically relevant parameters of the invasive process. The performance of our landscape-ABC method is assessed using simulated data sets differing in their information content (genetic and/or historical data). We apply our methodology to the recent introduction and spatial expansion of the cane toad, Bufo marinus, in northern Australia. We find that, at least in the context of cane toad invasion, historical data are more informative than genetic data for discriminating between introduction scenarios. However, the combination of historical and genetic data provides the most accurate estimates of demographic parameters. For the cane toad, we find some evidence for a strong bottleneck prior to introduction, a small initial number of founder individuals (about 15), a large population growth rate (about 400% per generation), a standard deviation of dispersal distance of 19 km per generation and a high invasion speed at equilibrium (50 km per year). Our approach strengthens the application of the ABC method to the field of bioinvasion by allowing statistical inferences to be made on the introduction and the spatial expansion dynamics of invasive species using a combination of various relevant sources of information.