Using ab initio electronic structure calculations, we have investigated the effect of epitaxial strain on magnetocrystalline anisotropy (MCA) of Ta/FeCo/MgO heterostructure. At small expansive strains on the FeCo layer, the system exhibits perpendicular MCA (PMA). Strain not only has a profound effect on the value of MCA but also induces a switching of magnetic easy axis. Analysis of the energy- and k-resolved distribution of orbital characters of the minority-spin band reveals that a significant contribution to PMA at zero strain arises from the spin-orbit coupling between occupied d x 2 − y 2 and unoccupied dxy states, derived from Fe at the FeCo/MgO interface. The strain effect is attributed to strain-induced shifts of spin-orbit coupled d-states. Our work demonstrates that strain engineering can open a viable pathway towards tailoring magnetic properties for spintronic applications.