Common basin models assume that the post‐rift tectonic evolution of most basins is usually associated with tectonic quiescence. However, tectonic inversion during the post‐rift phase has been proposed for several sedimentary basins worldwide, but how and why it happens is still a matter of debate, especially in intracontinental settings where the lithosphere is old and thick. Here, we use geological and geophysical data from the Rio do Peixe Basin in NE Brazil to show evidence that intracontinental sedimentary basins can be tectonically inverted by far‐field compressive stresses acting on pre‐existing weakness zones of lithospheric‐scale where stresses can concentrate and inversion can occur. Geomorphological and field data combined with seismic reflection, gravimetric and borehole data show that: (a) inversion occurred along two main Precambrian lithospheric‐scale shear zones, the Patos (E‐W trending) and Portalegre (NE‐SW trending), which had already been reactivated as basin‐bounding faults during the earlier rift stage; (b) post‐rift reactivation affected (mostly) the original master normal faults with the largest rift displacements, and locally produced new reverse faults; (c) during contraction, deformation was partitioned between fault reactivation and buckling of the incompetent sediment pushed against the hard basement; (d) all these signs of inversion have been observed in the field and can be demonstrated on seismic reflection profiles; and (e) combined gravimetric and seismic data show that the main structures of the basin were followed by an inversion. These data are consistent with the operation of WSW‐ENE horizontal maximum compressive stress as a result of combined pushes of the Mid‐Atlantic Ridge (towards the W) and the Andes (towards the E), responsible for the post‐rift oblique inversion of normal faults inherited from the rift phase and formed with vertical maximum compressive stress.