To describe microscopic hydrogen migration processes and steps of hydride formation we have carried out a theoretical study of the hydrogen diffusion in hexagonal closed packed (hcp), body-centered cubic (bcc), and face-centered cubic (fcc) Mg-lattices. To determine the preferable hydrogen diffusion pathways the activation energy E_a along the minimum energy path between two hydrogen positions were calculated. The hydrogen diffusion coefficient at 673 K for hcp-Mg was found to be equal to 1.11 × 10⁻⁸ m²/s that is in fair agreement with experiment data. The calculations of the hydrogen migration in Mg lattices have shown that bcc-Mg exhibits the lowest activation energy and, as the result, the highest diffusion coefficient. Taking into account that the bcc-Mg structure does not share the so-called blocking layer effect, we consider that this structure should promote fast hydrogen diffusion. On the bases of the present theoretical study, as well from previous calculations and experimental data we propose a scheme of structural hydrogen induced phase transformations in magnesium.