The production of high-purity hydrogen from hydrogen storage materials with further direct use of generated hydrogen in fuel cells is still a relevant research field. For this purpose, nickel-molybdenum-plated copper catalysts (NiMo/Cu), comprising between 1 and 20 wt.% molybdenum, as catalytic materials for hydrogen generation, were prepared using a low-cost, straightforward electroless metal deposition method by using citrate plating baths containing Ni2+–Mo6+ ions as a metal source and morpholine borane as a reducing agent. The catalytic activity of the prepared NiMo/Cu catalysts toward alkaline sodium borohydride (NaBH4) hydrolysis increased with the increase in the content of molybdenum present in the catalysts. The hydrogen generation rate of 6.48 L min−1 gcat−1 was achieved by employing NiMo/Cu comprising 20 wt.% at a temperature of 343 K and a calculated activation energy of 60.49 kJ mol−1 with remarkable stability, retaining 94% of its initial catalytic activity for NaBH4 hydrolysis following the completion of the fifth cycle. The synergetic effect between nickel and molybdenum, in addition to the formation of solid-state solutions between metals, promoted the hydrogen generation reaction.