The ^124-131Te nuclei have been produced as fission fragments in two fusion reactions induced by heavy ions ( ¹²C + ²³⁸U at 90MeV bombarding energy and ¹⁸O + ²⁰⁸Pb at 85MeV) and studied with the Euroball array. Their high-spin level schemes have been extended up to 6MeV (even-A and 5MeV (odd-A excitation energies from the triple -ray coincidence data. The - angular correlations have been analyzed in order to assign spin and parity values to most of the observed states. Moreover the half-lives of isomeric states have been measured from the delayed coincidences between the fission-fragment detector SAPhIR and Euroball, as well as from the timing information of the Ge detectors. The behaviors of the yrast structures identified in the present work are first discussed in comparison with the general features known in the mass region, particularly the breakings of neutron pairs occupying the h _11/2 orbit identified in the neighboring Sn nuclei. The experimental level schemes are then compared to shell-model calculations performed in this work. The analysis of the wave functions shows the effects of the proton-pair breaking along the yrast lines of the heavy Te isotopes.