The wide continental margin of southern Louisiana borders Paleozoic terranes that accreted to Laurentia before Jurassic rifting formed the Gulf of Mexico. It is unclear whether continental rifting here involved widespread or localized crustal extension, or how seafloor spreading in the Gulf of Mexico started. To improve our understanding of this rifting episode, we gathered marine seismic-refraction data along a 396-km-long transect from the continental shelf 50 km off the western Louisiana coast to the central ocean basin as part of the Gulf of Mexico Basin Opening (GUMBO) program. Using travel-time tomography, we imaged the compressional seismic-velocity structure from the shallow sediments to the uppermost mantle. In our geophysical model, the crust tapers in thickness from ~11 km near the Louisiana coast to ~8 km in the deep water of the central Gulf of Mexico. The compressional seismic velocity increases from 5.7 to 5.9 km/s in the shallow basement to 6.8-7.2 km/s above the Moho. The thickness and average wave speed of crust beneath the modern Louisiana coast and continental shelf suggest the presence of uniformly stretched continental crust that was intruded by mantle-derived melts during extension before continental breakup. South of the Sigsbee Escarpment, the crust is thinner with a higher seismic velocity, which is more consistent with thick oceanic crust. A comparison of our seismic-velocity model with coincident seismic-reflection data indicates that the voluminous Louann Salt was likely deposited on rifted continental crust shortly before the onset of seafloor spreading in the Gulf of Mexico.