Atomistic descriptions of the μ-opioid receptor (μOR) noncovalently binding with two of its prototypical morphinan agonists, morphine (MOP) and hydromorphone (HMP), are investigated using molecular dynamics (MD) simulations. Subtle differences between the binding modes and hydration properties of MOP and HMP emerge from the calculations. Alchemical free energy perturbation calculations show qualitative agreement with in vitro experiments performed in this work: indeed, the binding free energy difference between MOP and HMP computed by forward and backward alchemical transformation is 1.2±1.1 and 0.8±0.8 kcal/mol, respectively, to be compared with 0.4±0.3 kcal/mol from experiment. Comparison with an MD simulation of μOR covalently bound with the antagonist β-funaltrexamine hints to agonist-induced conformational changes associated with an early event of the receptor's activation: a shift of the transmembrane helix 6 relative to the transmembrane helix 3 and a consequent loss of the key R165-T279 interhelical hydrogen bond. This finding is consistent with a previous proposal suggesting that the R165-T279 hydrogen bond between these two helices indicates an inactive receptor conformation.