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The human genome contains hundreds of thousands of regions harboring copy-number variants (CNV). However, the phenotypic effects of most such polymorphisms are unknown because only larger CNVs have been ascertainable from SNP-array data generated by large biobanks. We developed a computational approach leveraging haplotype sharing in biobank cohorts to more sensitively detect CNVs. Applied to UK Biobank, this approach accounted for approximately half of all rare gene inactivation events produced by genomic structural variation. This CNV call set enabled a detailed analysis of associations between CNVs and 56 quantitative traits, identifying 269 independent associations (p  5 Ã— 10) likely to be causally driven by CNVs. Putative target genes were identifiable for nearly half of the loci, enabling insights into dosage sensitivity of these genes and uncovering several gene-trait relationships. These results demonstrate the ability of haplotype-informed analysis to provide insights into the genetic basis of human complex traits.