In this article we argue that the broad diffusion of renewables such as solar and wind power in the global energy system will probably require the development of efficient systems for the storage of excess electricity produced during off-peak hours. We also point out that in many places on Earth wood is a type of biomass that is available in large quantities as by-product of agricultural and industrial activities, which could be valorized through gasification processes that produce syngas. We combine these two observations by presenting an analysis of a power-to-gas system in which hydrogen obtained via electrolysis is used for the hydrogasification of wood. This process produces a synthetic natural gas (SNG) mixture that consists mostly of methane with only minor impurities of hydrogen. We show that the SNG generated in this sustainable way represents an efficient means for renewable energy storage. We also study wood hydrogasification processes with hydrogen production methods alternative to electrolysis, such as the partial oxidation of biomass, the water gas shift reaction, and the Sabatier reaction. We determine the process operating conditions that maximize the SNG yield and energy efficiency. Through an economic assessment we examine the applicability of the process to a plant located in Northern Italy. In all process types SNG exhibits characteristics that comply with methane grid quality requirements. We conclude that SNG production through wood hydrogasification can compete with methane market prices when using zero-cost renewable electricity produced during off-peak hours.