Dengue and yellow fever have complex cycles, involving urban and sylvatic mosquitoes, and non‐human primate hosts. To date, efforts to assess the effect of climate change on these diseases have neglected the combination of such crucial factors. Recent studies only considered urban vectors. This is the first study to include them together with sylvatic vectors and the distribution of primates to analyse the effect of climate change on these diseases. We used previously published models, based on machine learning algorithms and fuzzy logic, to identify areas where climatic favourability for the relevant transmission agents could change: 1) favourable areas for the circulation of the viruses due to the environment and to non‐human primate distributions; 2) the favourability for urban and sylvatic vectors. We obtained projections of future transmission risk for two future periods and for each disease, and implemented uncertainty analyses to test for predictions reliability. Areas currently favourable for both diseases could keep being climatically favourable, while global favourability could increase a 7% for yellow fever and a 10% increase for dengue. Areas likely to be more affected in the future for dengue include West Africa, South Asia, the Gulf of Mexico, Central America and the Amazon basin. A possible spread of dengue could take place into Europe, the Mediterranean basin, the UK and Portugal; and, in Asia, into northern China. For yellow fever, climate could become more favourable in Central and Southeast Africa; India; and in north and southeast South America, including Brazil, Paraguay, Bolivia, Peru, Colombia and Venezuela. In Brazil, favourability for yellow fever will probably increase in the south, the west and the east. Areas where the transmission risk spread is consistent to the dispersal of vectors are highlighted in respect of areas where the expected spread is directly attributable to environmental changes. Both scenarios could involve different prevention strategies.