We present structural and magnetic properties of three sets of structures: as-deposited CoPt films cosputtered at 900 K on MgO(110) substrates with a Pt(110) buffer layer and CoPt films deposited by molecular beam epitaxy directly on MgO(110) substrates at 900 K, as prepared and annealed at 900 K. All layers have the L10 tetragonal structure. The chemical long-range ordering for the as-deposited CoPt films is incomplete in contrast with the annealed CoPt films, where long-range order is the highest. The structural study of these CoPt films grown on MgO(110) has pointed out that three variants of the L10 phase coexist. The proportion of x and y variants, with the concentration modulation along a vector oriented at 45° with respect to the growth direction, is higher than the proportion of the z variant with the concentration modulation within the plane. The magnetic study shows an in-plane easy magnetization axis with a large magnetic anisotropy. This is interesting for the magnetic recording media with classical longitudinal writing and reading heads. The simulation of the magnetization loops confirms that the easy magnetization axis is within the plane and along the  direction, favored by the dominant x and y variants.