In this registry‐based cohort study, we estimated the risk of human papillomavirus (HPV)‐related anogenital premalignancies and cancer in renal transplant recipients (RTRs) compared to a nontransplanted comparison cohort. We identified all first‐time RTRs in Denmark during 1990–2015 in a nationwide nephrology register. For each RTR, we randomly selected 50 age‐ and sex‐matched non‐RTRs from the background population. The study population was followed for diagnoses of cervical, vaginal, vulvar, penile and anal intraepithelial neoplasia grades 2–3 (IN2/3) and cancer for up to 27 years. We estimated hazard ratios (HRs) of anogenital IN2/3 and cancer in RTRs vs. non‐RTRs by Cox regression separately for men and women using age as underlying timescale, adjusting for income, education, HPV vaccination and immunocompromising conditions. We included 4,261 RTRs and 213,673 non‐RTRs. RTRs had increased hazard of cervical (HR = 2.1, 95% CI: 1.7–2.8), vaginal (HR = 35.0, 95% CI: 13.9–87.7), vulvar (HR = 16.4, 95% CI: 10.4–25.8), penile (HR = 21.9, 95% CI: 11.1–43.5) and anal (women: HR = 51.1, 95% CI: 28.0–93.1; men: HR = 39.0, 95% CI: 16.7–91.1) IN2/3. The HRs of anogenital cancers were also increased at most sites. The HR of anogenital IN2/3 in female RTRs tended to be higher during graft function than during dialysis. In female RTRs aged <40 years at transplantation, 10–15% had cervical IN2/3 and 5–12% had vaginal/vulvar/anal IN2/3 within 20 years after transplantation, compared to 4–8 and 0.2–0.4%, respectively, of female non‐RTRs. In conclusion, RTRs had substantially higher risk of HPV‐related anogenital premalignancies and cancer than non‐RTRs.