The effect of ambient humidity on the electrical conductivity of α-Ga2O3 and α-Ga2O3/ε-Ga2O3 is investigated. Polymorphic epitaxial Ga2O3 layers are deposited by the method of chloride vapor-phase epitaxy on sapphire substrates. The contacts are made of Pt and Pt/Ti. It is discovered that the I–V characteristics of the Pt/α-Ga2O3/Pt and Pt/Ti/α-Ga2O3/ε-Ga2O3/Ti/Pt structures have a high sensitivity to atmospheric humidity in the temperature range of 25–100°C. It is found that the effect of water vapor on the I–V characteristics is reversible, and the most significant current changes in the samples are observed at a relative humidity of RH ≥ 60%. As the temperature rises, the effect of atmospheric humidity on the I–V characteristics decreases and disappears at temperatures of T > 100°C. The experimental results obtained are explained within the framework of the Grotthuss mechanism.