Optical waveguides are fabricated by irradiation of LiTaO3 with a variety of swift heavy ions that provide increasing levels of both nuclear and electronic damage rates, including C, F and Si ions, in the energy range of 15-40 MeV. A systematic study of the role of the ion fluence has been carried out in the broad range of 1e13-2e15 at/cm2. The kinetics of damage is initially of nuclear origin for the lowest fluences and stopping powers and, then, is enhanced by the electronic excitation (for F and Si ions) in synergy with the nuclear damage. Applying suitable annealing treatments, optical propagation losses values as low as 0.1 dB have been achieved. The damage rates found in LiTaO3 have been compared with those known for the reference LiNbO3 and discussed in the context of the thermal spike model.