Pterois volitans and Pterois miles, two sub-species of lionfish, have become the first non-native, invasive marine fish established along the United States Atlantic coast and Caribbean. The route and timing of the invasion is poorly understood, however historical sightings and captures have been robustly documented since their introduction. Herein we analyze these records based on spatial location, dates of arrival, and prevailing physical factors at the capture sights. Using a cellular automata model, we examine the relationship between depth, salinity, temperature, and current, finding the latter as the most influential parameter for transport of lionfish to new areas. The model output is a synthetic validated reproduction of the lionfish invasion, upon which predictive simulations in other locations can be based. This predictive model is simple, highly adaptable, relies entirely on publicly available data, and is applicable to other species.