Genome-wide association studies (GWAS) yield large numbers of genetic loci associated with traits and diseases. Predicting the effector genes that mediate these locus-trait associations remains challenging. Here we present the FLAMES (fine-mapped locus assessment model of effector genes) framework, which predicts the most likely effector gene in a locus. FLAMES creates machine learning predictions from biological data linking single-nucleotide polymorphisms to genes, and then evaluates these scores together with gene-centric evidence of convergence of the GWAS signal in functional networks. We benchmark FLAMES on gene-locus pairs derived by expert curation, rare variant implication and domain knowledge of molecular traits. We demonstrate that combining single-nucleotide-polymorphism-based and convergence-based modalities outperforms prioritization strategies using a single line of evidence. Applying FLAMES, we resolve the FSHB locus in the GWAS for dizygotic twinning and further leverage this framework to find schizophrenia risk genes that converge with rare coding evidence and are relevant in different stages of life.