Visceral leishmaniasis (VL) is an important neglected disease caused by a protozoan parasite, and represents a serious public health problem in many parts of the world. It is zoonotic in Europe and Latin America, where infected dogs constitute the main domestic reservoir for the parasite and play a key role in VL transmission to humans. In Brazil this disease is caused by the protozoan Leishmania infantum chagasi, and is transmitted by the sand fly Lutzomyia longipalpis. Despite programs aimed at eliminating infection sources, the disease continues to spread throughout the Country. VL in São Paulo State, Brazil, first appeared in the northwestern region, spreading in a southeasterly direction over time. We integrate data on the VL vector, infected dogs and infected human dispersion from 1999 to 2013 through an innovative spatial temporal Bayesian model in conjunction with geographic information system. This model is used to infer the drivers of the invasion process and predict the future progression of VL through the State. We found that vector dispersion was influenced by vector presence in nearby municipalities at the previous time step, proximity to the Bolívia-Brazil gas pipeline, and high temperatures (i.e., annual average between 20 and 23°C). Key factors affecting infected dog dispersion included proximity to the Marechal Rondon Highway, high temperatures, and presence of the competent vector within the same municipality. Finally, vector presence, presence of infected dogs, and rainfall (approx. 270 to 540mm/year) drove the dispersion of human VL cases. Surprisingly, economic factors exhibited no noticeable influence on disease dispersion. Based on these drivers and stochastic simulations, we identified which municipalities are most likely to be invaded by vectors and infected hosts in the future. Prioritizing prevention and control strategies within the identified municipalities may help halt the spread of VL while reducing monitoring costs. Our results contribute important knowledge to public and animal health policy planning, and suggest that prevention and control strategies should focus on vector control and on blocking contact between vectors and hosts in the priority areas identified to be at risk.