Fracture zone trends and magnetic anomalies in the Atlantic Ocean indicate that the North American plate must have moved with respect to the South American plate during the opening of the Atlantic. A comparison of plate tectonic flow lines with fracture zones identified from Geosat and Seasat altimeter data suggests that the North American‐South American plate boundary migrated northward from die Guinea‐Demarara shear margin to the Vema Fracture Zone before chron 34 (84 Ma), to north of the Doldrums Fracture Zone before chron 22 (51.9 Ma), and to north of the Mercurius Fracture Zone between chron 32 (72.5 Ma) and chron 13 (35.5 Ma). The paleoridge offset through time identified from magnetic anomalies and the computed cumulative strike slip motion in the plate boundary area, indicate that the triple junction may have been located between the Mercurius and the Fifteen‐Twenty fracture zones after 67 Ma (chron 30). Plate reconstructions indicate a Late Cretaceous phase of transtension, followed by transpression in the Tertiary for the Tiburon/Barracuda Ridge area south of the Fifteen‐Twenty Fracture Zone. The ocean floor in this area is characterized by a series of ridges and troughs with large Bouguer gravity anomalies (up to ∼135 mGal). We use smoothing spline estimation to invert Bouguer anomalies for crustal layer structure. Our model results suggest that the Moho is uplifted 2–4 km over short wavelengths (∼70 km) at the Barracuda and Tiburon ridges and imply large anelastic strains. The severely thinned crust at the two ridges implies that crustal extension must have taken place before they were uplifted. We propose that the North‐South American plate boundary migrated to the latitude of the Tiburon Ridge, bounded by the Vema and Marathon fracture zones, before chron 34 (84 Ma). Post‐chron 34 crustal thinning during a transtensional tectonic regime may have been localized at preexisting structural weaknesses such as the Vema, Marathon, Mercurius, and Fifteen‐Twenty fracture zone troughs, but reaching the Fifteen‐Twenty Fracture Zone and future Barracuda Ridge area only after chron 32 (72.5 Ma). This interpretation concurs with our crustal structural model, which shows stronger crustal thinning underneath the Tiburon Ridge than at the Barracuda Ridge. Subsequent transpression may have continued along the existing zones of weakness in the Tertiary, creating the presently observed crustal deformation and uplift of the Moho, accompanied by anelastic failure of the crust. Middle‐Eocene‐Upper Oligocene turbidites on the slope of the Tiburon Ridge, now located 800 m above the abyssal plain, suggest that most of its uplift occurred at post‐Oligocene times. The unusually shallow Moho underneath the Tiburon and Barracuda ridges represents an unstable density distribution, which may indicate that compressive stresses are still present to maintain these anomalies, and that the North American‐South American plate boundary may still be located in this area.