Magnetic and multiferroic nanocomposites with two distinct phases have been a topic of intense research for their profound potential applications in the field of spintronics. In addition to growing high-quality phase separated heteroepitaxial nanocomposites, the strain engineering that is conducive to enhance the tunability of material properties, in general, and the magnetic properties, in particular, is of utmost importance in exploring new possibilities. Here, we investigated the magneto-structural coupling between antiferromagnetic BiFeO3 (BFO) and ferrimagnetic CoFe2O4 (CFO) in self-assembled vertically aligned nanocomposites grown on LaAlO3 (LAO) and SrTiO3 (STO) substrates. We found that BFO exhibits tetragonal (T) and rhombohedral (R) structures as the stable phases and CFO has high magnetocrystalline anisotropy even in the form of nanocomposites. The temperature and magnetic field dependent magnetizations of T_BFO-CFO/LAO and R_BFO-CFO/STO nanocomposites primarily demonstrate the magnetoelastic coupling between these variants.