Epithelial tissues can elongate in two dimensions by polarized cell intercalation, oriented cell division, or cell shape change, owing to local or global actomyosin contractile forces acting in the plane of the tissue. In addition, epithelia can undergo morphogenetic change in three dimensions. We show that elongation of the wings and legs of Drosophila involves a columnar-to-cuboidal cell shape change that reduces cell height and expands cell width. Remodeling of the apical extracellular matrix by the Stubble protease and basal matrix by MMP1/2 proteases induces wing and leg elongation. Matrix remodeling does not occur in the haltere, a limb that fails to elongate. Limb elongation is made anisotropic by planar polarized Myosin-II, which drives convergent extension along the proximal-distal axis. Subsequently, Myosin-II relocalizes to lateral membranes to accelerate columnar-to-cuboidal transition and isotropic tissue expansion. Thus, matrix remodeling induces dynamic changes in actomyosin contractility to drive epithelial morphogenesis in three dimensions.