This Letter presents the first direct experimental measurements of the damping of Toroidicity induced Alfvén Eigenmodes (TAE), carried out in the JET tokamak. These measurements were obtained during the first experiments to drive these modes with antennas external to a tokamak plasma. Different regimes corresponding to different dominant TAE absorption mechanisms with a wide range of damping rates,  10-3 ≤ γ/ω ≤ 10-1, have been identified in ohmically heated plasma discharges using this new active diagnostic for Alfvén eigenmodes.