Hydrolysis of MgH2 has a high theoretical hydrogen yield (15.2%) and is very attractive for onsite hydrogen production. However, the low solubility of Mg(OH)2 causes sluggish kinetics and incomplete utilization of MgH2. In this paper, we solve this problem by using organic acids (acetic, citric and oxalic) and nanoscale graphene-like carbon. The organic acid solution significantly increases the yield and rate of H2 generation due to its acidic nature. The hydrogen yield approaches 100% with a fast hydrolysis rate when the molar ratio Acid/MgH2 exceeds 0.9, 2.0 and 2.7 for the citric, oxalic and acetic acid, respectively. In doing so, pH of the reaction solutions after hydrolysis corresponds to 4.53, 2.11 and 4.28, accordingly, testifying about buffer nature of the solutions “citric acid / magnesium citrate” and “acetic acid / magnesium acetate”. The addition of graphene-like material (GLM) also significantly increases the yield and rate of H2 generation due to the decrease of particle size and increase of defects in the material, as well as due to stabilising the MgH2 nanoparticles and preventing their agglomeration. Additionally, GLM encapsulates the MgH2 particles thus suppressing the formation of MgO and, in turn, promoting achievement of the maximum hydrogen yield. In addition, this work presents layout and operation features of the developed apparatus for the controlled generation of pressurised hydrogen using hydrolysis of Mg or MgH2 in acidic solutions, as well as its testing results for the hydrolysis of Mg and MgH2 in the solution of citric acid.