Estimates of the spatiotemporal distribution of different mosquito vector species and the associated risk of transmission of arboviruses are key to design adequate policies for preventing local outbreaks and reducing the number of human infections in endemic areas. In this study, we quantified the abundance of Aedes albopictus and Aedes aegypti and the local transmission potential for three arboviral infections at an unprecedented spatiotemporal resolution in areas where no entomological surveillance is available. We developed a computational model to quantify the daily abundance of Aedes mosquitoes, leveraging temperature and precipitation records. The model was calibrated on mosquito surveillance data collected in 115 locations in Europe and the Americas between 2007 and 2018. Model estimates were used to quantify the reproduction number of dengue virus, Zika virus, and chikungunya in Europe and the Americas, at a high spatial resolution. In areas colonised by both Aedes species, A aegypti was estimated to be the main vector for the transmission of dengue virus, Zika virus, and chikungunya, being associated with a higher estimate of R0 when compared with A albopictus. Our estimates highlighted that these arboviruses were endemic in tropical and subtropical countries, with the highest risks of transmission found in central America, Venezuela, Colombia, and central-east Brazil. A non-negligible potential risk of transmission was also estimated for Florida, Texas, and Arizona (USA). The broader ecological niche of A albopictus could contribute to the emergence of chikungunya outbreaks and clusters of dengue autochthonous cases in temperate areas of the Americas, as well as in mediterranean Europe (in particular, in Italy, southern France, and Spain). Our results provide a comprehensive overview of the transmission potential of arboviral diseases in Europe and the Americas, highlighting areas where surveillance and mosquito control capacities should be prioritised. EU and Ministero dell'Università e della Ricerca, Italy (Piano Nazionale di Ripresa e Resilienza Extended Partnership initiative on Emerging Infectious Diseases); EU (Horizon 2020); Ministero dell'Università e della Ricerca, Italy (Progetti di ricerca di Rilevante Interesse Nazionale programme); Brazilian National Council of Science, Technology and Innovation; Ministry of Health, Brazil; and Foundation of Research for Minas Gerais, Brazil.