Density-functional calculations are performed to predict structural and magnetic properties of (001) BiFeO3 films under tensile epitaxial strain. These films remain monoclinic (Cc space group) for misfit strains between 0% and 8%, with the polarization, tilt axis and magnetization all rotating when varying the strain. At a tensile strain 8%, these films undergo a first-order phase transition towards an orthorhombic phase (Ima2 space group). In this novel phase, the polarization and tilt axis lie in the epitaxial plane, while the magnetization is along the out-of-plane direction and the direction of the antiferromagnetic vector is unchanged by the phase transition. An unexpected additional degree of freedom, namely, an antiphase arrangement of Bi atoms, is also found for all tensile strains