Ferroelectric ferromagnets are exceedingly rare, fundamentally interesting multiferroic materials that could give rise to new technologies in which the low power and high speed of field-effect electronics are combined with the permanence and routability of voltage-controlled ferromagnetism1, 2. Furthermore, the properties of the few compounds that simultaneously exhibit these phenomena1, 2, 3, 4, 5 are insignificant in comparison with those of useful ferroelectrics or ferromagnets: their spontaneous polarizations or magnetizations are smaller by a factor of 1,000 or more. The same holds for magnetic- or electric-field-induced multiferroics6, 7, 8. Owing to the weak properties of single-phase multiferroics, composite and multilayer approaches involving strain-coupled piezoelectric and magnetostrictive components are the closest to application today1, 2. Recently, however, a new route to ferroelectric ferromagnets was proposed9 by which magnetically ordered insulators that are neither ferroelectric nor ferromagnetic are transformed into ferroelectric ferromagnets using a single control parameter, strain. The system targeted, EuTiO3, was predicted to exhibit strong ferromagnetism (spontaneous magnetization, ~7 Bohr magnetons per Eu) and strong ferroelectricity (spontaneous polarization, ~10µCcm−2) simultaneously under large biaxial compressive strain9. These values are orders of magnitude higher than those of any known ferroelectric ferromagnet and rival the best materials that are solely ferroelectric or ferromagnetic. Hindered by the absence of an appropriate substrate to provide the desired compression we turned to tensile strain. Here we show both experimentally and theoretically the emergence of a multiferroic state under biaxial tension with the unexpected benefit that even lower strains are required, thereby allowing thicker high-quality crystalline films. This realization of a strong ferromagnetic ferroelectric points the way to high-temperature manifestations of this spin–lattice coupling mechanism10. Our work demonstrates that a single experimental parameter, strain, simultaneously controls multiple order parameters and is a viable alternative tuning parameter to composition11 for creating multiferroics.