Human Papillomavirus 16 (HPV16) causes 70% of invasive cervical cancers (ICC) worldwide. Interaction between HPV16 genetic diversity, host genetics and target tissue largely determine the chances to trigger carcinogenesis. We have analyzed the differential prevalence of viral variants in 233 HPV16‐monoinfected squamous (SCC), glandular (ADC) and mixed (ADSC) ICCs from four continents, assessing the contribution of geographical origin and cancer histology. We have further quantified the contribution of viral variants and cancer histology to differences in age at tumor diagnosis. The model fitted to the data explained 97% of the total variance: the largest explanatory factors were differential abundance among HPV16 variants (78%) and their interaction with cancer histology (9.2%) and geography (10.1%). HPV16_A1‐3 variants were more prevalent in SCC while HPV16_D variants were increased in glandular ICCs. We confirm further a non‐random geographical structure of the viral variants distribution. ADCs were diagnosed at younger ages than SCCs, independently of the viral variant triggering carcinogenesis. HPV16 variants are differentially associated with histological ICCs types, and ADCs are systematically diagnosed in younger women. Our results have implications for the implementation of cervical cancer screening algorithms, to ensure proper early detection of elusive ADCs. What's new? Interaction between Human Papillomavirus 16 genetic diversity, host genetics and target tissue largely determines the odds of HPV16 triggering invasive cervical cancers (ICCs), but the mechanisms remain unclear. Our study assessed HPV16 variant diversity in three ICC histological types in European, Central‐South American, Asian and African samples. Different viral variants displayed different prevalence depending on geographical origin and histological cancer type. Genuine differences in HPV16 lineage prevalence explained more than 70% of all variance in the viral lineage distribution, with the interaction of geographical origin and histological cancer type with HPV16 variants together accounting for 20% of the data variance.