Osteoporosis is a devastating disease with an essential genetic component. GWAS have discovered genetic signals robustly associated with bone mineral density (BMD), but not the precise localization of effector genes. Here, we carry out physical and direct variant to gene mapping in human mesenchymal progenitor cell-derived osteoblasts employing a massively parallel, high resolution Capture C based method in order to simultaneously characterize the genome-wide interactions of all human promoters. By intersecting our Capture C and ATAC-seq data, we observe consistent contacts between candidate causal variants and putative target gene promoters in open chromatin for ~ 17% of the 273 BMD loci investigated. Knockdown of two novel implicated genes, ING3 at 'CPED1-WNT16' and EPDR1 at 'STARD3NL', inhibits osteoblastogenesis, while promoting adipogenesis. This approach therefore aids target discovery in osteoporosis, here on the example of two relevant genes involved in the fate determination of mesenchymal progenitors, and can be applied to other common genetic diseases.