The epidermal growth factor receptor (EGFR) is a dimeric membrane protein that regulates key aspects of cellular function. Activation of the EGFR is linked to changes in the conformation of the transmembrane (TM) domain, brought about by changes in interactions of the TM helices of the membrane lipid bilayer. Using an advanced computational approach that combines Coarse-Grained molecular dynamics and well-tempered Meta Dynamics (CG-MetaD), we characterize the large-scale motions of the TM helices, simulating multiple association and dissociation events between the helices in membrane, thus leading to a free energy landscape of the dimerization process. The lowest energy state of the TM domain is a right-handed dimer structure in which the TM helices interact through the N-terminal small-X-3-small sequence motif. In addition to this state, which is thought to correspond to the active form of the receptor, we have identified further low-energy states that allow us to integrate with a high level of detail a range of previous experimental observations. These conformations may lead to the active state via two possible activation pathways, which involve pivoting and rotational motions of the helices, respectively. Molecular dynamics also reveals correlation between the conformational changes of the TM domains and of the intracellular juxtamembrane domains, paving the way for a comprehensive understanding of EGFR signaling at the cell membrane.