Florida faces the challenge of repeated introduction and autochthonous transmission of arboviruses transmitted by Aedes aegypti and Aedes albopictus. Empirically-based predictive models of the spatial distribution of these species would aid surveillance and vector control efforts. To predict the occurrence and abundance of these species, we fit a mixed-effects zero-inflated negative binomial regression to a mosquito surveillance dataset with records from more than 200,000 trap days, representative of 53% of the land area and ranging from 2004 to 2018 in Florida. We found an asymmetrical competitive interaction between adult populations of Aedes aegypti and Aedes albopictus for the sampled sites. Wind speed was negatively associated with the occurrence and abundance of both vectors. Our model predictions show high accuracy (72.9% to 94.5%) in validation tests leaving out a random 10% subset of sites and data since 2017, suggesting a potential for predicting the distribution of the two Aedes vectors.