We report growth of various phase architectures of self-assembled BiFeO3-CoFe2O4 (BFO-CFO) thin films on differently oriented SrTiO3 (STO) substrates. CFO forms segregated square, stripe, and triangular nanopillars embedded in a coherent BFO matrix on (001)-, (110)-, and (111)-oriented STO substrates, respectively. Nanostructures with an aspect ratio of up to 5:1 with a prominent magnetic anisotropy were obtained on both (001) and (110) STO along out-of-plane and in-plane directions. Magnetic easy axis rotation from in-plane to out-of-plane directions was realized through aspect ratio control. An intractable in-plane anisotropy was fixed in CFO on (111) STO due to the triangular shape of the ferromagnetic phase nanopillars. These studies established a detailed relationship of magnetic anisotropy with specific shape and dimensions of ordered magnetic arrays. The results suggest a way to effectively control the magnetic anisotropy in patterned ferromagnetic oxide arrays with tunable shape, aspect ratio, and elastic strain conditions of the nanostructures.