North Africa is now recognized as a major area for the emergence and dispersal of anatomically modern humans from at least 315 kya. The Mediterranean Basin is thus particularly suited to study the role of climate versus human-mediated changes on the evolutionary history of species. The Algerian mouse (Mus spretus Lataste) is an endemic species from this basin, with its distribution restricted to North Africa (from Libya to Morocco), Iberian Peninsula and South of France. A rich paleontological record of M. spretus exists in North Africa, suggesting hypotheses concerning colonization pathways, and the demographic and morphologic history of this species. Here we combined genetic (3 mitochondrial DNA loci and 18 microsatellites) and climatic niche modeling data to infer the evolutionary history of the Algerian mouse. We collected 646 new individuals in 51 localities. Our results are consistent with an anthropogenic translocation of the Algerian mouse from North Africa to the Iberian Peninsula via Neolithic navigators, probably from the Tingitane Peninsula. Once arrived in Spain, suitable climatic conditions would then have favored the dispersion of the Algerian mice to France. The morphological differentiation observed between Spanish, French and North African populations could be explained by a founder effect and possibly local adaptation. This article helps to better understand the role of climate versus human-mediated changes on the evolutionary history of mammal species in the Mediterranean Basin.