Evidence of how human evolution shaped the polygenicity of human traits and diseases has been extensively studied in populations of European descent. However, limited information is currently available about its impact on other ancestry groups. Here, we investigated how different evolutionary processes affected the common variant heritability of traits and diseases in East Asians. Leveraging genome-wide association statistics from the Biobank Japan (up to 158,284 participants), we assessed natural selection (negative and positive), archaic introgression from Neanderthal and Denisova, and several genomic functional categories with respect to the heritability of physiological and pathological conditions. Similar to reports in European descent populations, the heritability estimates for East Asian traits were ubiquitously enriched for negative selection annotations (false discovery rate, FDR q<0.05). Enrichment of Denisovan introgression was identified in coronary artery disease (1.69-fold enrichment, p=0.003). We followed up these enrichments by conducting a phenome-wide association study (PheWAS) of Denisovan and Neanderthal alleles in participants of six ancestral backgrounds from the UK Biobank. In East Asians, Denisovan-inherited alleles were associated with 22 phenotypes, including metabolic, immunological, cardiovascular, endocrine, and dermatological traits. The strongest association was observed for the Denisovan-inherited locus rs59185462 with rheumatoid arthritis (beta=0.82, p=1.91x10-105). In summary, our study provides the first evidence regarding the impact of evolutionary processes on the genetics of complex traits in worldwide populations, highlighting the specific contribution of Denisovan introgression in East Asian populations.