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Extensive research has recently been devoted to examination of surface nanovariation mediated magnetism and its utility, which has been demonstrated in one-dimensional surface modulation. In this work, we demonstrate an ability to control the anisotropy in continuous magnetic films by periodic surface modulation in two-dimensions. Magnetic properties of films with nano-modulated surfaces have been studied as a function of both film thickness and modulation amplitude. For films with a patterned square array, a clear fourfold-symmetry of anisotropy field and coercivity was observed with rotation angle. An experimental phase diagram of anisotropy with respect to film thickness and modulation amplitude has been produced. Micromagnetic simulation shows that the observed magnetic anisotropy is the consequence of minimization of magnetostatic energy.