By combining experimental and computational studies, the orthorhombic stannide CeMgSn with a TiNiSi-type structure has been characterized as a potential hydrogen storage material. Experimental studies of the formed monohydride CeMgSnH including hydrogen absorption-desorption, thermal desorption spectroscopy, synchrotron and neutron powder diffraction (298 and 2 K), magnetization, and ¹¹⁹Sn Mössbauer spectroscopic measurements are discussed in parallel with ab initio electronic structure calculations. A small, 1.27 vol %, expansion of the unit cell of CeMgSn during its transformation into a thermally stable CeMgSnH monohydride is caused by an ordered insertion of H atoms into half of the available Ce₃Mg tetrahedral interstices leaving the CeMg₃ tetrahedra unoccupied. The bonding in CeMgSnH is dominated by strong Ce-Sn and Mg-Sn interactions which are almost not altered by hydrogenation, whereas the H atoms carry a small negative charge and show bonding interactions with Ce and Mg. Hydrogenation causes a conversion of the antiferromagnetic CeMgSn into ferromagnetic CeMgSnH with the Ce moments aligned along [001] with a magnetic moment of 1.4(3) μ_B. The ¹¹⁹Sn isomer shifts and the values of quadrupole splitting in the Mössbauer spectra suggest a similar s-electron density distribution for the Ce- and La-containing REMgSnH monohydrides.