Chromatin structure is a key determinant of gene expression in eukaryotes, but it has not been possible to define the structure of cis-regulatory elements at the scale of the proteins that bind them. Here, we generate multidimensional chromosome conformation capture (3C) maps at base-pair resolution using Micro Capture-C ultra (MCCu). This can resolve contacts between individual transcription factor motifs within cis-regulatory elements. Using degron systems, we show that removal of Mediator complex components alters fine-scale promoter structure and that nucleosome depletion plays a key role in transcription factor-driven enhancer-promoter contacts. We observe that chromatin is partitioned into nanoscale domains by nucleosome-depleted regions. This structural conformation is reproduced by chemically specific coarse-grained molecular dynamics simulations of the physicochemical properties of chromatin. Combining MCCu with molecular dynamics simulations and super-resolution microscopy allows us to propose a unified model in which the biophysical properties of chromatin orchestrate contacts between cis-regulatory elements.