In order to resolve an outstanding discrepancy between experiment and theory regarding the ground-state structure of Mg(BH4)2, we examine the importance of long-range dispersive interactions on the compounds thermodynamic stability. Careful treatment of the correlation effects within a recently developed nonlocal van der Waals density functional (vdW-DF) leads to a good agreement with experiment, favoring the {alpha}-Mg(BH4)2 phase (P6122) and a closely related Mn(BH4)2-prototype phase (P3112) over a large set of polymorphs at low temperatures. Our study demonstrates the need to go beyond (semi)local density functional approximations for a reliable description of crystalline high-valent metal borohydrides.