Despite explosive growth in genomic datasets, the methods for studying epigenomic mechanisms of gene regulation remain primitive. Here we present a model-based approach to systematically analyze the epigenomic functions in modulating transcription factor-DNA binding. Based on the first principles of statistical mechanics, this model considers the interactions between epigenomic modifications and a cis-regulatory module, which contains multiple binding sites arranged in any configurations. We compiled a comprehensive epigenomic dataset in mouse embryonic stem (mES) cells, including DNA methylation (MeDIP-seq and MRE-seq), DNA hydroxymethylation (5-hmC-seq), and histone modifications (ChIP-seq). We discovered correlations of transcription factors (TFs) for specific combinations of epigenomic modifications, which we term epigenomic motifs. Epigenomic motifs explained why some TFs appeared to have different DNA binding motifs derived from in vivo (ChIP-seq) and in vitro experiments. Theoretical analyses suggested that the epigenome can modulate transcriptional noise and boost the cooperativity of weak TF binding sites. ChIP-seq data suggested that epigenomic boost of binding affinities in weak TF binding sites can function in mES cells. We showed in theory that the epigenome should suppress the TF binding differences on SNP-containing binding sites in two people. Using personal data, we identified strong associations between H3K4me2/H3K9ac and the degree of personal differences in NFκB binding in SNP-containing binding sites, which may explain why some SNPs introduce much smaller personal variations on TF binding than other SNPs. In summary, this model presents a powerful approach to analyze the functions of epigenomic modifications. This model was implemented into an open source program APEG (<underline>A</underline>ffinity <underline>P</underline>rediction by <underline>E</underline>pigenome and <underline>G</underline>enome, <ext-link ext-link-type="uri" xlink:href="http://systemsbio.ucsd.edu/apeg" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink">http://systemsbio.ucsd.edu/apeg</ext-link>).