Direct measurement of the remanent polarization of high quality (001)-oriented epitaxial ${\mathrm{BiFeO}}_{3}$ thin films shows a strong strain dependence, even larger than conventional (001)-oriented ${\mathrm{PbTiO}}_{3}$ films. Thermodynamic analysis reveals that a strain-induced polarization rotation mechanism is responsible for the large change in the out-of-plane polarization of (001) ${\mathrm{BiFeO}}_{3}$ with biaxial strain while the spontaneous polarization itself remains almost constant.