Nearby genes are often expressed as a group. Yet, the prevalence, molecular mechanisms and genetic control of local gene co-expression are far from being understood. Here, by leveraging gene expression measurements across 49 human tissues and hundreds of individuals, we find that local gene co-expression occurs in 13% to 53% of genes per tissue. By integrating various molecular assays (e.g. ChIP-seq and Hi-C), we estimate the ability of several mechanisms, such as enhancer-gene interactions, in distinguishing gene pairs that are co-expressed from those that are not. Notably, we identify 32,636 expression quantitative trait loci (eQTLs) which associate with co-expressed gene pairs and often overlap enhancer regions. Due to affecting several genes, these eQTLs are more often associated with multiple human traits than other eQTLs. Our study paves the way to comprehend trait pleiotropy and functional interpretation of QTL and GWAS findings. All local gene co-expression identified here is available through a public database ( https://glcoex.unil.ch/ ).