The majority of variants identified by genome-wide association studies (GWAS) reside in the noncoding genome, affecting regulatory elements including transcriptional enhancers. However, characterizing their effects requires the integration of GWAS results with context-specific regulatory activity and linkage disequilibrium annotations to identify causal variants underlying noncoding association signals and the regulatory elements, tissue contexts, and target genes they affect. We propose INFERNO, a novel method which integrates hundreds of functional genomics datasets spanning enhancer activity, transcription factor binding sites, and expression quantitative trait loci with GWAS summary statistics. INFERNO includes novel statistical methods to quantify empirical enrichments of tissue-specific enhancer overlap and to identify co-regulatory networks of dysregulated long noncoding RNAs (lncRNAs). We applied INFERNO to two large GWAS studies. For schizophrenia (36,989 cases, 113,075 controls), INFERNO identified putatively causal variants affecting brain enhancers for known schizophrenia-related genes. For inflammatory bowel disease (IBD) (12,882 cases, 21,770 controls), INFERNO found enrichments of immune and digestive enhancers and lncRNAs involved in regulation of the adaptive immune response. In summary, INFERNO comprehensively infers the molecular mechanisms of causal noncoding variants, providing a sensitive hypothesis generation method for post-GWAS analysis. The software is available as an open source pipeline and a web server.