Yes. The vaccine has been proven, through numerous studies, to prevent the infections that can cause multiple HPV cancers. In addition, population studies in the U.S. and other countries that have introduced the HPV vaccine have shown a significant reduction in abnormal Pap test results ^13,14 and genital warts. ^15,16

Sources:

13 Pollock KGJ, Kavanagh K, Potts A, et al. Reduction of low- and high-grade cervical abnormalities associated with high uptake of the HPV bivalent vaccine in Scotland. Br J Cancer. 2014;111(9):1824-1830. doi: 10.1038/bjc.2014.479.

14 Baldur-Felskov B, Dehlendorff C, Munk C, Kjaer SK. Early impact of human papillomavirus vaccination on cervical neoplasia – Nationwide follow-up of young Danish women. J Natl Cancer Inst. 2014;106(3):djt460. doi: 10.1093/jnci/djt460.

15 Ali H, Donovan B, Wand H, et al. Genital warts in young Australians five years into national human papillomavirus vaccination programme: national surveillance data. BMJ. 2013;346:f2032. doi: 10.1136/bmj.f2032.

16 Bauer HM, Wright G, Chow J. Evidence of human papillomavirus vaccine effectiveness in reducing genital warts: an analysis of California public family planning administrative claims data, 2007-2010. Am J Public Health. 2012;102(5):833-835. doi: 10.2105/AJPH.2011.300465.