Genes regulated by the same miRNA can be discovered by virtue of their coexpression at the transcriptional level and the presence of a conserved miRNA-binding site in their 3' UTRs. Using this principle we have integrated the three best performing and complementary algorithms into a framework for inference of regulation by miRNAs (FIRM) from sets of coexpressed genes. We demonstrate the utility of FIRM by inferring a cancer-miRNA regulatory network through the analysis of 2240 gene coexpression signatures from 46 cancers. By analyzing this network for functional enrichment of known hallmarks of cancer we have discovered a subset of 13 miRNAs that regulate oncogenic processes across diverse cancers. We have performed experiments to test predictions from this miRNA-regulatory network to demonstrate that miRNAs of the miR-29 family (miR-29a, miR-29b, and miR-29c) regulate specific genes associated with tissue invasion and metastasis in lung adenocarcinoma. Further, we highlight the specificity of using FIRM inferences to identify miRNA-regulated genes by experimentally validating that miR-767-5p, which partially shares the miR-29 seed sequence, regulates only a subset of miR-29 targets. By providing mechanistic linkage between miRNA dysregulation in cancer, their binding sites in the 3'UTRs of specific sets of coexpressed genes, and their associations with known hallmarks of cancer, FIRM, and the inferred cancer miRNA-regulatory network will serve as a powerful public resource for discovery of potential cancer biomarkers.