Wadsleyite, β-Mg2SiO4, is an important high pressure mineral that may act as a sink of water in the Earth's transition zone. In this study, we first determine the heat capacity and entropy of anhydrous wadsleyite at ambient pressure both experimentally and by first principles simulations. The measured standard entropy S0 at 298 K is 86.7(11) J/(mol K). Then, extended simulations are performed to explore the effect of pressure and hydration on these thermodynamic properties. The stability of several structural models of hydrogen incorporation is investigated and the lowest energy structures are used to derive the vibrational entropy and the heat capacity of hydrous wadsleyite with a nominal content of 1.6 and 3.3 wt% H2O at an ambient pressure and at 15 GPa. Considering an estimation of the configurational entropy, S0 of hydrous wadsleyite with 1.6 and 3.3 wt% H2O is predicted to be about 3.5 and 5 J/(mol K) higher than that of anhydrous wadsleyite at the ambient pressure.