Due to the need of transition probabilities for heavy ions, including those of tellurium, in different fields of physics and in astrophysics, we have investigated theoretically the atomic structure of two selected tellurium ions (Te+ and Te++) for which no theoretical data were available so far. The first transition probabilities have been calculated for the electric dipole (E1) transitions with wavelengths shorter than 1 micrometer in Te II-III. Both the multiconfiguration Dirac-Hartree-Fock (MCDHF) method and the relativistic Hartree-Fock (HFR) approach, in which core-polarization (CPOL) effects were included, have been used for the calculations. Results. The results obtained with these two completely independent methods are in reasonable agreement. As a consequence, the transition probabilities obtained in this work are expected to be reliable. They fill in a gap concerning the radiative parameters in these two ions.