Genome-wide association studies have identified thousands of single nucleotide variants and small indels that contribute to variation in hematologic traits. While structural variants are known to cause rare blood or hematopoietic disorders, the genome-wide contribution of structural variants to quantitative blood cell trait variation is unknown. Here we utilized whole genome sequencing data in ancestrally diverse participants of the NHLBI Trans Omics for Precision Medicine program (N = 50,675) to detect structural variants associated with hematologic traits. Using single variant tests, we assessed the association of common and rare structural variants with red cell-, white cell-, and platelet-related quantitative traits and observed 21 independent signals (12 common and 9 rare) reaching genome-wide significance. The majority of these associations (N = 18) replicated in independent datasets. In genome-editing experiments, we provide evidence that a deletion associated with lower monocyte counts leads to disruption of an S1PR3 monocyte enhancer and decreased S1PR3 expression.