Cytoplasmic dynein is a dimeric motor that transports intracellular cargoes towards the minus end of microtubules (MTs). In contrast to other processive motors, stepping of the dynein motor domains (heads) is not precisely coordinated. Therefore, the mechanism of dynein processivity remains unclear. Here, by engineering the mechanical and catalytic properties of the motor, we show that dynein processivity minimally requires a single active head and a second inert MT-binding domain. Processivity arises from a high ratio of MT-bound to unbound time, and not from interhead communication. In addition, nucleotide-dependent microtubule release is gated by tension on the linker domain. Intramolecular tension sensing is observed in dynein's stepping motion at high interhead separations. On the basis of these results, we propose a quantitative model for the stepping characteristics of dynein and its response to chemical and mechanical perturbation.