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Background: Aedes-borne arboviruses cause both seasonal epidemics and emerging outbreaks with a significant impact on global health. These viruses share mosquito vector species, often infecting the same host population within overlapping geographic regions. Thus, comparative analyses of the virus evolutionary and epidemiological dynamics across spatial and temporal scales could reveal convergent trends. Methodology/Principal findings: Focusing on Mexico as a case study, we generated novel chikungunya and dengue (CHIKV, DENV-1 and DENV-2) virus genomes from an epidemiological surveillance-derived historical sample collection, and analysed them together with longitudinally-collected genome and epidemiological data from the Americas. Aedes-borne arboviruses endemically circulating within the country were found to be introduced multiple times from lineages predominantly sampled from the Caribbean and Central America. For CHIKV, at least thirteen introductions were inferred over a year, with six of these leading to persistent transmission chains. For both DENV-1 and DENV-2, at least seven introductions were inferred over a decade. Conclusions/Significance: Our results suggest that CHIKV, DENV-1 and DENV-2 in Mexico share evolutionary and epidemiological trajectories. The southwest region of the country was determined to be the most likely location for viral introductions from abroad, with a subsequent spread into the Pacific coast towards the north of Mexico. Virus diffusion patterns observed across the country are likely driven by multiple factors, including mobility linked to human migration from Central towards North America. Considering Mexico's geographic positioning displaying a high human mobility across borders, our results prompt the need to better understand the role of anthropogenic factors in the transmission dynamics of Aedes-borne arboviruses, particularly linked to land-based human migration. Author summary: Mexico is endemic to several Aedes-borne arboviruses relevant to global health, and ranks within the top five countries in the Americas that report the highest case numbers. Our study provides a general overview of arbovirus introduction, spread and establishment patterns in North and Central America, and should be of interest to both local health and global authorities. Moreover, it sets to explore the paradigm of convergence at different scales in independent virus populations, represented by comparable epidemiological and evolutionary trends in Aedes-borne arboviruses sharing ecological niches. Our results represent important advances in the study of mosquito-borne viruses listed as a threat to global health, specifically applied to key countries within the developing world. [ABSTRACT FROM AUTHOR]