The reorientational dynamics of ammonium borohydride (NH4BH4) was studied using quasielastic neutron scattering in the temperature interval from 10 to 240 K, which covers both the dynamically ordered and disordered polymorphs of NH4BH4. In the low-temperature (<50K) ordered polymorph of NH4BH4, analysis of the quasielastic neutron scattering data reveals that no reorientational dynamics is present within the probed timescale region of 0.1 to 100 ps. In the high-temperature (>50K) disordered polymorph, the analysis establishes the onset of NH+4 and BH−4 dynamics at around 50 and 125 K, respectively. The relaxation time at 150 K for NH+4 is approximately 1 ps, while around 100 ps for BH−4. The NH+4 dynamics at temperatures below 125 K is associated with preferential tetrahedral tumbling motions, where each of the hydrogen atoms in the NH+4 tetrahedron can visit any of the four hydrogen sites, however, reorientations around a specific axis are more frequently occurring (C2 or C3). At higher temperatures, the analysis does not exclude a possible evolution of the NH+4 dynamics from tetrahedral tumbling to either cubic tumbling, where the hydrogen atoms can visit any of the eight positions corresponding to the corners of a cube, or isotropic rotational diffusion, where the hydrogen atoms can visit any location on the surface of a sphere. The BH−4 dynamics can be described as cubic tumbling. The difference in reorientational dynamics between the two ions is related to the difference of the local environment where the dynamically much slower BH−4 anion imposes a noncubic environment on the NH+4 cation.