In this work, we propose the Bilayer Graphene Tunnel Field Effect Transistor (BG-TFET) as a device suitable for fabrication and circuit integration with present-day technology. It provides high Ion/Ioff ratio at ultra-low supply voltage, without the limitations in terms of prohibitive lithography and patterning requirements for circuit integration of graphene nanoribbons. Our investigation is based on the solution of the coupled Poisson and Schroedinger equations in three dimensions, within the Non-Equilibrium Green (NEGF) formalism on a Tight Binding Hamiltonian. We show that the small achievable gap of only few hundreds meV is still enough for promising TFET operation, providing a large Ion/Ioff ratio in excess of 10^3 even for a supply voltage of only 0.1 V. Key to this performance is the low quantum capacitance of bilayer graphene, which permits to obtain an extremely small sub-threshold swing S smaller than 20 mV/decade at room temperature.