An elevated resting heart rate (RHR) is associated with increased cardiovascular mortality. Genome-wide association studies (GWAS) have identified > 350 loci. Uniquely, in this study we applied genetic fine-mapping leveraging tissue specific chromatin segmentation and colocalization analyses to identify causal variants and candidate effector genes for RHR. We used RHR GWAS summary statistics from 388,237 individuals of European ancestry from UK Biobank and performed fine mapping using publicly available genomic annotation datasets. High-confidence causal variants (accounting for > 75% posterior probability) were identified, and we collated candidate effector genes using a multi-omics approach that combined evidence from colocalisation with molecular quantitative trait loci (QTLs), and long-range chromatin interaction analyses. Finally, we performed druggability analyses to investigate drug repurposing opportunities. The fine mapping pipeline indicated 442 distinct RHR signals. For 90 signals, a single variant was identified as a high-confidence causal variant, of which 22 were annotated as missense. In trait-relevant tissues, 39 signals colocalised with cis-expression QTLs (eQTLs), 3 with cis-protein QTLs (pQTLs), and 75 had promoter interactions via Hi-C. In total, 262 candidate genes were highlighted (79% had promoter interactions, 15% had a colocalised eQTL, 8% had a missense variant and 1% had a colocalised pQTL), and, for the first time, enrichment in nervous system pathways. Druggability analyses highlighted ACHE, CALCRL, MYT1 and TDP1 as potential targets. Our genetic fine-mapping pipeline prioritised 262 candidate genes for RHR that warrant further investigation in functional studies, and we provide potential therapeutic targets to reduce RHR and cardiovascular mortality.