Autozygosity is associated with rare Mendelian disorders and clinically-relevant quantitative traits. We investigated associations between FROH(fraction of the genome in runs of homozygosity) and common diseases in Genes & Health (N=23,978 British South Asians), UK Biobank (N=397,184), and 23andMe, Inc. We show that restricting analysis to offspring of first cousins is an effective way of removing confounding due to social/environmental correlates of FROH. Within this group in G&H+UK Biobank, we found experiment-wide significant associations between FROHand twelve common diseases. We replicated the associations with type 2 diabetes (T2D) and post-traumatic stress disorder via between-sibling analysis in 23andMe (median N=480,282). We estimated that autozygosity due to consanguinity accounts for 5-18% of T2D cases amongst British Pakistanis. Our work highlights the possibility of widespread non-additive effects on common diseases and has important implications for global populations with high rates of consanguinity.