Short tandem repeats (STRs) have been implicated in a variety of complex traits in humans. However, genome-wide studies of the effects of STRs on gene expression thus far have had limited power to detect associations and provide insights into putative mechanisms. Here, we leverage whole-genome sequencing and expression data for 17 tissues from the Genotype-Tissue Expression Project to identify more than 28,000 STRs for which repeat number is associated with expression of nearby genes (eSTRs). We use fine-mapping to quantify the probability that each eSTR is causal and characterize the top 1,400 fine-mapped eSTRs. We identify hundreds of eSTRs linked with published genome-wide association study signals and implicate specific eSTRs in complex traits, including height, schizophrenia, inflammatory bowel disease and intelligence. Overall, our results support the hypothesis that eSTRs contribute to a range of human phenotypes, and our data should serve as a valuable resource for future studies of complex traits.