Morphogenesis of the respiratory appendages on eggshells of Drosophila species provides a powerful experimental system for studying how cell sheets give rise to complex three-dimensional structures. In Drosophila melanogaster, each of the two tubular eggshell appendages is derived from a primordium comprising two distinct cell types. Using live imaging and three-dimensional image reconstruction, we demonstrate that the transformation of this two-dimensional primordium into a tube involves out-of-plane bending followed by a sequence of spatially ordered cell intercalations. These morphological transformations correlate with the appearance of complementary distributions of myosin and Bazooka in the primordium. These distributions suggest that a two-dimensional pattern of line tensions along cell-cell edges on the apical side of the epithelium is sufficient to produce the observed changes in morphology. Computational modeling shows that this mechanism could explain the main features of tissue deformation and cell rearrangements observed during three-dimensional morphogenesis.