Human genetic studies have provided substantial insight into the biological mechanisms governing ovarian ageing, yet previous approaches have been largely restricted to assessing common genetic variation. Here we report analyses of rare (MAF<0.1%) protein-coding variants in the exomes of 106,973 women from the UK Biobank study, implicating novel genes with effect sizes up to ~5 times larger than previously discovered in analyses of common variants. These include protein truncating variants in ZNF518A, which shorten reproductive lifespan by promoting both earlier age at natural menopause (ANM, 5.61 years [4.04-7.18], P=2*10-12) and later puberty timing in girls (age at menarche, 0.56 years [0.15-0.97], P=9.2*10-3). By integrating ChIP-Seq data, we demonstrate that common variants associated with ANM and menarche are enriched in the binding sites of ZNF518A. We also identify further links between ovarian ageing and cancer susceptibility, highlighting damaging germline variants in SAMHD1 that delay ANM and increase all-cause cancer risk in both males (OR=2.1 [1.7-2.6], P=4.7*10-13) and females (OR=1.61 [1.31-1.96], P=4*10-6). Finally, we demonstrate that genetic susceptibility to earlier ovarian ageing in women increases de novo mutation rate in their offspring. This provides direct evidence that female mutation rate is heritable and highlights an example of a mechanism for the maternal genome influencing child health.