We calculate ab initio the NMR relaxation rates and the Knight shifts in MgB2. We show that the dominant relaxation mechanism at the B-11 nucleus is the interaction with the electronic orbital moment, and we give a simple explanation of that using a simple sp tight-binding model. When Stoner enhancement (also calculated ab initio) is accounted for, we obtain good agreement with reported experimental values. For the Mg-25 nucleus, we predict that the dominant relaxation mechanism is the Fermi-contact interaction, which also dominates the Mg Knight shift.