Eukaryotic cells commonly use protein kinases in signaling systems that relay information and control a wide range of processes. These enzymes have a fundamentally similar structure, but achieve functional diversity through variable regions that determine how the catalytic core is activated and recruited to phosphorylation targets. "Hippo" pathways are ancient protein kinase signaling systems that control cell proliferation and morphogenesis; the NDR/LATS family protein kinases, which associate with "Mob" coactivator proteins, are central but incompletely understood components of these pathways. Here we describe the crystal structure of budding yeast Cbk1-Mob2, to our knowledge the first of an NDR/LATS kinase-Mob complex. It shows a novel coactivator-organized activation region that may be unique to NDR/LATS kinases, in which a key regulatory motif apparently shifts from an inactive binding mode to an active one upon phosphorylation. We also provide a structural basis for a substrate docking mechanism previously unknown in AGC family kinases, and show that docking interaction provides robustness to Cbk1's regulation of its two known in vivo substrates. Co-evolution of docking motifs and phosphorylation consensus sites strongly indicates that a protein is an in vivo regulatory target of this hippo pathway, and predicts a new group of high-confidence Cbk1 substrates that function at sites of cytokinesis and cell growth. Moreover, docking peptides arise in unstructured regions of proteins that are probably already kinase substrates, suggesting a broad sequential model for adaptive acquisition of kinase docking in rapidly evolving intrinsically disordered polypeptides.