The offset ridge-transform structure of ocean basins is one of the most prominent expressions of plate tectonics. Yet why this configuration is favored over a continuous divergent boundary has remained unresolved. We examine this issue using mantle Bouguer anomalies (MBAs) from contrasting ridge systems in the North Atlantic. The Reykjanes Ridge north of the Bight transform fault has no transform offsets and is characterized by rapidly propagating melting centers along a linear axis and a continuous MBA low. To the south, the adjoining Mid-Atlantic Ridge has typical ridge segments each underlain by a discrete MBA “bulls-eye” low and offset by transform and non-transform discontinuities. We hypothesize that the pattern of mantle melting, as reflected in the MBAs, creates chemical and rheologic variations in the residual mantle that either favor or hinder transform fault formation. Within ridge segments, mantle melting efficiently extracts water producing dry and strong residual mantle. At segment ends, low extents of melting and inefficient melt extraction preserve damp and weak mantle. On the linear Reykjanes Ridge continuous melting and rapidly propagating melting centers create continuous strong mantle with possibly weak rheologic variations at high angles to the opening direction, not favoring transform faults. In contrast, stable segmented mantle melting on the Mid-Atlantic Ridge forms bands of strong and weak residual mantle aligned in the spreading direction, the latter creating favorable locations for shear deformation and transform faults. Our hypothesis also explains the lack of transform faults at Earth's endmember spreading rates. At ultra-slow ridges, overall melting is limited and irregular and melt extraction is inefficient. At ultra-fast ridges, mantle melting is pervasive and melt extraction is efficient. In both cases, organized spreading-parallel compositional rheological variations do not form and transform faults are not favored. Our model implies that beyond cooling and strengthening with age, the pattern of mantle melting shapes the rheological structure of oceanic lithosphere and the geometry of plate tectonics.