Human papillomavirus (HPV) types 16/18, included in HPV vaccines, contribute to the majority of cervical cancer, and a substantial proportion of cervical intraepithelial neoplasia (CIN) grades 2/3 or worse (CIN2+/CIN3+) including adenocarcinoma in situ or worse. The aim of this study was to quantify the effect of quadrivalent HPV (qHPV) vaccination on incidence of CIN2+ and CIN3+. A nationwide cohort of girls and young women resident in Sweden 2006-2013 and aged 13-29 (n = 1,333,691) was followed for vaccination and histologically confirmed high-grade cervical lesions. Data were collected using the Swedish nationwide healthcare registers. Poisson regression was used to calculate incidence rate ratios (IRRs) and vaccine effectiveness [(1-IRR)x100%] comparing fully vaccinated with unvaccinated individuals. IRRs were adjusted for attained age and parental education, and stratified on vaccination initiation age. Effectiveness against CIN2+ was 75% (IRR = 0.25, 95%CI = 0.18-0.35) for those initiating vaccination before age 17, and 46% (IRR = 0.54, 95%CI = 0.46-0.64) and 22% (IRR = 0.78, 95%CI = 0.65-0.93) for those initiating vaccination at ages 17-19, and at ages 20-29, respectively. Vaccine effectiveness against CIN3+ was similar to vaccine effectiveness against CIN2+. Results were robust for both women participating to the organized screening program and for women at prescreening ages. We show high effectiveness of qHPV vaccination on CIN2+ and CIN3+ lesions, with greater effectiveness observed in girls younger at vaccination initiation. Continued monitoring of impact of HPV vaccination in the population is needed in order to evaluate both long-term vaccine effectiveness and to evaluate whether the vaccination program achieves anticipated effects in prevention of invasive cervical cancer.