Rare genetic variants are abundant across the human genome, and identifying their function and phenotypic impact is a major challenge. Measuring aberrant gene expression has aided in identifying functional, large-effect rare variants (RVs). Here, we expanded detection of genetically driven transcriptome abnormalities by analyzing gene expression, allele-specific expression, and alternative splicing from multitissue RNA-sequencing data, and demonstrate that each signal informs unique classes of RVs. We developed Watershed, a probabilistic model that integrates multiple genomic and transcriptomic signals to predict variant function, validated these predictions in additional cohorts and through experimental assays, and used them to assess RVs in the UK Biobank, the Million Veterans Program, and the Jackson Heart Study. Our results link thousands of RVs to diverse molecular effects and provide evidence to associate RVs affecting the transcriptome with human traits.