The effect of electron confinement on the magnetocrystalline anisotropy of ultrathin bcc Fe films is explored by combining photoemission spectroscopy, x-ray magnetic circular dichroism, and magnetooptical Kerr effect measurements. Pronounced thickness-dependent variations in the magnetocrystalline anisotropy are ascribed to periodic changes in the density of states at the Fermi level, induced by quantization of d_xz, d_yz out-of-plane orbitals. Our results reveal a direct correlation between quantum well states, the orbital magnetic moment, and the magnetocrystalline anisotropy.