We present a combined experimental and theoretical study on electronic and magnetic properties of the Fe(001)-p(1x1)O surface. The ordered p(1x1) surface is investigated with spin-polarized scanning tunneling microscopy and spectroscopy accompanied by first-principles calculations. The atomic registry of the Fe(001)-p(1x1)O surface was confirmed in real space from the atomically resolved images. Tunneling spectroscopy reveals two oxygen induced features in the local density of states, around -0.7 eV and at the Fermi level, the origin of which is discussed based on first-principles calculations. Due to the hybridization of oxygen pz states with the Fe states near the Fermi level, the spin polarization in tunneling experiments is inverted upon oxygen adsorption.