Interactions between transcription factors and chromatin are fundamental to genome organization and regulation and, ultimately, cell state. Here, we use information theory to measure signatures of organized chromatin resulting from transcription factor-chromatin interactions encoded in the patterns of the accessible genome, which we term chromatin information enrichment (CIE). We calculate CIE for hundreds of transcription factor motifs across human samples and identify two classes: low and high CIE. The 10-20% of common and tissue-specific high CIE transcription factor motifs, associate with higher protein-DNA residence time, including different binding site subclasses of the same transcription factor, increased nucleosome phasing, specific protein domains, and the genetic control of both chromatin accessibility and gene expression. These results show that variations in the information encoded in chromatin architecture reflect functional biological variation, with implications for cell state dynamics and memory.