We used cross-correlation of ambient noise records from seismic stations in the US, Mexico, and Cuba to extract dispersion data of Rayleigh surface wave. Our derived 3D shear-wave velocity model of the greater Gulf of Mexico (GOM) region captures variations in the crustal and lithospheric structures across the continental margins of the US Gulf Coast and Yucatan, Mexico. The model shows a zone of reduced velocity in the mantle lithosphere underlying the extended continental margin of the northwestern GOM. We attributed this velocity reduction to extensional deformation and melt-induced weakening of the lithosphere during the Triassic continental rifting that preceded the seafloor spreading that formed the GOM. Melt extraction might have been hindered by the greater lithospheric thickness in the western region along the US Gulf Coast margin that resulted in the westward decrease of rift-related volcanism/magmatism reported from previous studies. The clear asymmetry between the US Gulf Coast and its conjugate Yucatan margin suggests extension along a shear-zone that focused more deformation on the North American plate prior to breakup. In contrast to the counterclockwise rotation of the Yucatan block during seafloor-spreading, our analyses using deformable plate models demonstrate that continental rifting occurred in a predominantly northwest-southeast direction. This change in plate motion is attributed to the development of mantle shear-zones in the western part of the rift. We estimated the depth of the lithosphere-asthenosphere boundary and determined that the extended continental and oceanic lithospheres have mostly regained their thickness since the time of breakup.