Transform faults at mid-ocean ridges--one of the most striking, yet enigmatic features of terrestrial plate tectonics--are considered to be the inherited product of preexisting fault structures. Ridge offsets along these faults therefore should remain constant with time. Here, numerical models suggest that transform faults are actively developing and result from dynamical instability of constructive plate boundaries, irrespective of previous structure. Boundary instability from asymmetric plate growth can spontaneously start in alternate directions along successive ridge sections; the resultant curved ridges become transform faults within a few million years. Fracture-related rheological weakening stabilizes ridge-parallel detachment faults. Offsets along the transform faults change continuously with time by asymmetric plate growth and discontinuously by ridge jumps.