In plate kinematic reconstructions, the restoration of rifted margins and their fossil equivalents exposed in orogens remains challenging. Tight fit reconstructions rely on the mapping of margins rift domains, their restoration to their pre-rift crustal thickness, and the removal of the oceanic and exhumed mantle domains. At present-day margins, high-resolution wide-angle seismic imaging allows mapping and measurement of rift domains; however, restoring fossil margins is trickier because they are largely overprinted and partially lost during convergence. Here, we present a new kinematic model for the Mesozoic rifting along the Tethys-Atlantic junction, which relies on two assumptions: (1) the width of the fossil Alpine Tethys rift domains was comparable to that of their present-day analogs, and (2) the necking zones of the former tectonic plates can be mapped, dated and used as kinematic markers. This reproducible workflow allows us, for the first time, to restore the rifted margins of the Alpine Tethys. Our reconstruction shows: (1) a westward propagation of extension through the Ionian, Alpine Tethys and Pyrenean rift systems from the Triassic to the Cretaceous, (2) the segmentation of the Mesozoic Tethyan rifted margins by strike-slip corridors, (3) the opening of an oceanic gateway at 165 Ma as mantle was exhumed along the entire Alpine Tethys and (4) the subdivision of the Mesozoic oceanic domain into compartments that were later consumed during subduction. This new model is supported by published data from the Alps, the Ionian Sea, the Pyrenees and the southern North Atlantic.