Most variants associated with complex traits and diseases identified by genome-wide association studies (GWAS) map to noncoding regions of the genome with unknown effects. Using ancestrally diverse biobank-scale GWAS data, massively parallel CRISPR screens, and single cell transcriptomic and proteomic sequencing, we discovered 124 cis -target genes of 91 noncoding blood trait GWAS loci. Using precise variant insertion via base editing, we connected specific variants with gene expression changes. We also identified trans -effect networks of noncoding loci when cis target genes encoded transcription factors or microRNAs. Networks were themselves enriched for GWAS variants and demonstrated polygenic contributions to complex traits. This platform enables massively-parallel characterization of the target genes and mechanisms of human noncoding variants in both cis and trans .