The development of non-volatile logic through direct coupling of spontaneous ferroelectric polarization with semiconductor charge carriers is nontrivial, with many issues, including epitaxial ferroelectric growth, demonstration of ferroelectric switching and measurable semiconductor modulation. Here we report a true ferroelectric field effect-carrier density modulation in an underlying Ge(001) substrate by switching of the ferroelectric polarization in epitaxial c-axis-oriented BaTiO3 grown by molecular beam epitaxy. Using the density functional theory, we demonstrate that switching of BaTiO3 polarization results in a large electric potential change in Ge. Aberration-corrected electron microscopy confirms BaTiO3 tetragonality and the absence of any low-permittivity interlayer at the interface with Ge. The non-volatile, switchable nature of the single-domain out-of-plane ferroelectric polarization of BaTiO3 is confirmed using piezoelectric force microscopy. The effect of the polarization switching on the conductivity of the underlying Ge is measured using microwave impedance microscopy, clearly demonstrating a ferroelectric field effect.