Short tandem repeats (STRs) are genomic regions consisting of repeated sequences of 1-6 bp in succession. Single-nucleotide polymorphism (SNP)-based genome-wide association studies (GWASs) do not fully capture STR effects. To study these effects, we imputed 445,720 STRs into genotype arrays from 408,153 White British UK Biobank participants and tested for association with 44 blood phenotypes. Using two fine-mapping methods, we identify 119 candidate causal STR-trait associations and estimate that STRs account for 5.2%-7.6% of causal variants identifiable from GWASs for these traits. These are among the strongest associations for multiple phenotypes, including a coding CTG repeat associated with apolipoprotein B levels, a promoter CGG repeat with platelet traits, and an intronic poly(A) repeat with mean platelet volume. Our study suggests that STRs make widespread contributions to complex traits, provides stringently selected candidate causal STRs, and demonstrates the need to consider a more complete view of genetic variation in GWASs.