Cell motion inside dense tissues governs many biological processes, including embryonic development and cancer metastasis, and recent experiments suggest that these tissues exhibit collective glassy behavior. To make quantitative predictions about glass transitions in tissues, we study a self-propelled Voronoi model that simultaneously captures polarized cell motility and multibody cell-cell interactions in a confluent tissue, where there are no gaps between cells. We demonstrate that the model exhibits a jamming transition from a solidlike state to a fluidlike state that is controlled by three parameters: the single-cell motile speed, the persistence time of single-cell tracks, and a target shape index that characterizes the competition between cell-cell adhesion and cortical tension. In contrast to traditional particulate glasses, we are able to identify an experimentally accessible structural order parameter that specifies the entire jamming surface as a function of model parameters. We demonstrate that a continuum soft glassy rheology model precisely captures this transition in the limit of small persistence times and explain how it fails in the limit of large persistence times. These results provide a framework for understanding the collective solid-to-liquid transitions that have been observed in embryonic development and cancer progression, which may be associated with epithelial-to-mesenchymal transition in these tissues.