Complex diseases often have distinct mechanisms spanning multiple tissues. We propose tissue-gene fine-mapping (TGFM), which infers the posterior inclusion probability (PIP) for each gene-tissue pair to mediate a disease locus by analyzing summary statistics and expression quantitative trait loci (eQTL) data; TGFM also assigns PIPs to non-mediated variants. TGFM accounts for co-regulation across genes and tissues and models uncertainty in cis-predicted expression models, enabling correct calibration. We applied TGFM to 45 UK Biobank diseases or traits using eQTL data from 38 Genotype-Tissue Expression (GTEx) tissues. TGFM identified an average of 147 PIP > 0.5 causal genetic elements per disease or trait, of which 11% were gene-tissue pairs. Causal gene-tissue pairs identified by TGFM reflected both known biology (for example, TPO-thyroid for hypothyroidism) and biologically plausible findings (for example, SLC20A2-artery aorta for diastolic blood pressure). Application of TGFM to single-cell eQTL data from nine cell types in peripheral blood mononuclear cells (PBMCs), analyzed jointly with GTEx tissues, identified 30 additional causal gene-PBMC cell type pairs.