Production of fatty alcohols through selective hydrogenation of fatty acids was studied over a 4% ReOx/TiO2 catalyst. Stearic acid was hydrogenated to octadecanol at temperatures and pressures between 180–200 °C and 2–4 MPa, with selectivity reaching 93%. A high yield of octadecanol was attributed to a strong adsorption of the acid compared to alcohol on the catalyst, which inhibits further alcohol transformation to alkanes. Low amounts (<7%) of alkanes (mainly octadecane) were formed during the conversion of stearic acid. However, it was found that the catalyst could be tuned for the production of alkanes. The reaction intermediates were octadecanal and stearyl stearate. Based on the reaction products analysis and catalyst characterization, a reaction mechanism and possible pathways were proposed.