The aryl hydrocarbon receptor (AhR) is a ligand-activated transcription factor that mediates the biological and toxicological effects of structurally diverse chemicals, including halogenated aromatic hydrocarbons. In this work, we investigate the effects of the binding of the AhR prototypical ligand, TCDD, on the stability of the AhR:ARNT complex, as well as the mechanisms by which ligand-induced perturbations propagate to the DNA recognition site responsible for gene transcription. To this aim, a reliable structural model of the overall quaternary structure of the AhR:ARNT:DRE complex is proposed, based on homology modelling. The model shows very good agreement with a previous one and is supported by experimental evidence. Moreover, molecular dynamics simulations are performed to compare the dynamic behaviour of the AhR:ARNT heterodimer in the presence or absence of the TCDD. Analysis of the simulations, performed by an unsupervised machine learning method, shows that TCDD binding to the AhR PASB domain influences the stability of several inter-domain interactions, in particular at the PASA-PASB interface. The inter-domain communication network suggests a mechanism by which TCDD binding allosterically stabilizes the interactions at the DNA recognition site. These findings may have implications for the comprehension of the different toxic outcomes of AhR ligands and drug design.