The contribution of genome structural variation (SV) to quantitative traits associated with cardiometabolic diseases remains largely unknown. Here, we present the results of a study examining genetic association between SVs and cardiometabolic traits in the Finnish population. We used sensitive methods to identify and genotype 129,166 high-confidence SVs from deep whole-genome sequencing (WGS) data of 4,848 individuals. We tested the 64,572 common and low-frequency SVs for association with 116 quantitative traits and tested candidate associations using exome sequencing and array genotype data from an additional 15,205 individuals. We discovered 31 genome-wide significant associations at 15 loci, including 2 loci at which SVs have strong phenotypic effects: (1) a deletion of the ALB promoter that is greatly enriched in the Finnish population and causes decreased serum albumin level in carriers (p = 1.47 × 10^-54) and is also associated with increased levels of total cholesterol (p = 1.22 × 10^-28) and 14 additional cholesterol-related traits, and (2) a multi-allelic copy number variant (CNV) at PDPR that is strongly associated with pyruvate (p = 4.81 × 10^-21) and alanine (p = 6.14 × 10^-12) levels and resides within a structurally complex genomic region that has accumulated many rearrangements over evolutionary time. We also confirmed six previously reported associations, including five led by stronger signals in single nucleotide variants (SNVs) and one linking recurrent HP gene deletion and cholesterol levels (p = 6.24 × 10^-10), which was also found to be strongly associated with increased glycoprotein level (p = 3.53 × 10^-35). Our study confirms that integrating SVs in trait-mapping studies will expand our knowledge of genetic factors underlying disease risk.