The extent to which low-frequency (minor allele frequency (MAF) between 1-5%) and rare (MAF <= 1%) variants contribute to complex traits and disease in the general population is mainly unknown. Bone mineral density (BMD) is highly heritable, a major predictor of osteoporotic fractures, and has been previously associated with common genetic variants(1-8), as well as rare, population specific, coding variants(9). Here we identify novel non-coding genetic variants with large effects on BMD (n(total) = 53,236) and fracture (n(total) = 508,253) in individuals of European ancestry from the general population. Associations for BMD were derived from whole-genome sequencing (n = 2,882 from UK10K (ref. 10); a population-based genome sequencing consortium), whole-exome sequencing (n = 3,549), deep imputation of genotyped samples using a combined UK10K/1000 Genomes reference panel (n = 26,534), and de novo replication genotyping (n = 20,271). We identified a low-frequency non-coding variant near a novel locus, EN1, with an effect size fourfold larger than the mean of previously reported common variants for lumbar spine BMD8 (rs11692564(T), MAF51.6%, replication effect size510.20 s.d., P-meta = 2 x 10(-14)), which was also associated with a decreased risk of fracture (odds ratio = 0.85; P = 2 x 10(-11); ncases = 98,742 and ncontrols = 409,511). Using an En1cre/flox mouse model, we observed that conditional loss of En1 results in low bone mass, probably as a consequence of high bone turnover. We also identified a novel low frequency non-coding variant with large effects on BMD near WNT16 (rs148771817(T), MAF = 1.2%, replication effect size +10.41 s.d., P-meta = 1 x 10(-11)). In general, there was an excess of association signals arising from deleterious coding and conserved non-coding variants. These findings provide evidence that low-frequency non-coding variants have large effects on BMD and fracture, thereby providing rationale for whole-genome sequencing and improved imputation reference panels to study the genetic architecture of complex traits and disease in the general population.