Controlling magnetism by using electric fields is a goal of research towards novel spintronic devices and future nano-electronics. For this reason, multiferroic heterostructures attract much interest. Here we provide experimental evidence, and supporting DFT analysis, of a transition in La0.65Sr0.35MnO3 (LSMO) thin film to a stable ferromagnetic phase, that is induced by the structural and strain 2 properties of the ferroelectric BaTiO3 (BTO) substrate, which can be modified by applying external electric fields. X-ray Magnetic Circular Dichroism (XMCD) measurements on Mn L edges with a synchrotron radiation show, in fact two magnetic transitions as a function of temperature that correspond to structural changes of the BTO substrate. We also show that ferromagnetism, absent in the pristine condition at room temperature, can be established by electrically switching the BTO ferroelectric domains in the out-of-plane direction. The present results confirm that electrically induced strain can be exploited to control magnetism in multiferroic oxide heterostructures.