High-dimensional omics datasets provide valuable resources to determine the causal role of molecular traits in mediating the path from genotype to phenotype. Making use of molecular quantitative trait loci (QTL) and genome-wide association study (GWAS) summary statistics, we propose a multivariable Mendelian randomization (MVMR) framework to quantify the proportion of the impact of the DNA methylome (DNAm) on complex traits that is propagated through the assayed transcriptome. Evaluating 50 complex traits, we find that on average at least 28.3% (95% CI: [26.9%-29.8%]) of DNAm-to-trait effects are mediated through (typically multiple) transcripts in the cis-region. Several regulatory mechanisms are hypothesized, including methylation of the promoter probe cg10385390 (chr1:8'022'505) increasing the risk for inflammatory bowel disease by reducing PARK7 expression. The proposed integrative framework can be extended to other omics layers to identify causal molecular chains, providing a powerful tool to map and interpret GWAS signals.