Despite hundreds of reports involving both plants and animals, the mechanisms underlying introgression remain obscure, even if some form of selection is frequently invoked. Introgression has repeatedly been reported in species that have recently colonized a new habitat, suggesting that demographic processes should be given more attention for understanding the mechanisms of introgression. Here we show by spatially explicit simulations that massive introgression of neutral genes takes place during the invasion of an occupied territory if interbreeding is not severely prevented between the invading and the local species. We also demonstrate that introgression occurs almost exclusively from the local to the invading species, especially for populations located far away from the source of the invasion, and this irrespective of the relative densities of the two species. This pattern is strongest at markers experiencing reduced gene flow, in keeping with the observation that organelle genes are often preferentially introgressed across species boundaries. A survey of the literature shows that a majority of published empirical studies of introgression during range expansions, in animals and in plants, follow the predictions of our model. Our results imply that speciation genes can be identified by comparing genomes of interfertile native and invading species pairs.