Selective area epitaxy at the nanoscale enables fabrication of high-quality nanostructures in regular arrays with predefined geometry. Here, we investigate the growth mechanisms of GaAs nanoridges on GaAs (100) substrates in selective area trenches by metal-organic vapor-phase epitaxy (MOVPE). It is found that pre-growth annealing results in the formation of valley-like structures of GaAs with atomic terraces inside the trenches. MOVPE growth of GaAs nanoridges consists of three distinct stages. Filling the trench in the first stage exhibits a step-flow growth behavior. Once the structure grows above the mask surface, it enters the second stage of growth by forming {101} side facets as the (100) flat top facet progressively shrinks. In the third stage, the fully formed nanoridge begins to overgrow onto the mask with a significantly reduced growth rate. We develop a kinetic model that accurately describes the width-dependent evolution of the nanoridge morphology through all three stages. MOVPE growth of fully formed nanoridges takes only about 1 min, which is 60 times faster than in our set of molecular beam epitaxy (MBE) experiments reported recently, and with a more regular, triangular cross-sectional geometry defined solely by the {101} facets. In contrast to MBE, no material loss due to Ga adatom diffusion onto the mask surface is observed in MOVPE until the third stage of growth. These results are useful for the fabrication of GaAs nanoridges of different dimensions on the same substrate for various applications and can be extended to other material systems.