Ultrathin Co films have been electrodeposited onto Cu(001) single crystals from a deaerated aqueous electrolyte of 0.3 M Na2SO4 and 1 mM CoSO4. The films show the intrinsic magnetic properties of Co, as measured in situ, if the cleanliness conditions in the electrochemical cell are equivalent to ultrahigh vacuum conditions. The combination of magneto-optical Kerr effect (MOKE) measurements and surface X-ray diffraction with an electrochemical cell allows us to monitor in situ the magnetic hysteresis of the films, their epitaxial properties, their growth and dissolution, as well as their stability near the Nernst potential of Co2+/Co. Unlike with the scanning tunneling microscope, magnetic properties, as e.g. the coercivity, or structural properties of buried layers or the Co/Cu interface can be obtained, which complement the electrochemical measurements. Films thicker than 1.5 ML show their easy magnetization-axis in-plane and parallel [110]. The magnetic moment increases linearly with the film thickness. The measured magnetic anisotropies originate from the symmetry of the fee crystal structure and demonstrate the epitaxial growth of electrodeposited Co on Cu(001).