The sheathing leaf found in grasses and other monocots is an evolutionary innovation, yet its origin has been a subject of long-standing debate. Here, we revisit the problem in the light of developmental genetics and computational modeling. We show that the sheathing leaf likely arose through WOX-gene-dependent extension of a primordial zone straddling concentric domains around the shoot apex. Patterned growth within this zone, oriented by two polarity fields, accounts for wild-type, mutant and mosaic grass leaf development, whereas zone contraction and growth remodeling accounts for eudicot leaf development. In contrast to the prevailing view, our results suggest that the sheath derives from petiole, whereas the blade derives from the lamina of the eudicot leaf, consistent with homologies proposed in the 19th century.