Magnetostrictive effect in Ta/CoxFe100-x(B)[CoFe(B)]/MgO for alloy compositions spanning Fe-rich (x=20) to Co-rich (x=80) stacks has been studied to investigate the relation between magnetostrictive effect and the onset of perpendicular magnetic anisotropy at Ta/CoFe(B)/MgO interfaces. Interestingly, for each Co composition, a t-dependent crossover between in-plane (ip) and out-of-plane (op) magnetic anisotropy is found at a different CoFe(B) thickness (tcro)—denoted as crossover thickness, which means compositional variations of magnetic properties at the interfaces. By considering the Ta/CoFe(B) and CoFe(B)/MgO interfaces as atomistic volumes with ip and op orbital magnetizations, respectively, the relative ratio of ip to op orbital magnetization in the atomistic volumes is found to be closely related to the dependence of magnetostriction constant (λs) on the Co composition. The findings suggest that the composition dependence of ip and op orbital magnetization at the Ta/CoFe(B)/MgO interfaces plays an important role in controlling its interfacial anisotropy and magnetostrictive effect of the stacks with the interfaces.