Entangled states are a key resource in fundamental quantumphysics, quantum cryptography and quantum computation1. Introduction of controlled unitary processes—quantum gates—to a quantum system has so far been the most widely used method to create entanglement deterministically2. These processes require high-fidelity state preparation and minimization of the decoherence that inevitably arises fromcoupling between the systemand the environment, and imperfect control of the system parameters. Here we combine unitary processes with engineered dissipation to deterministically produce and stabilize an approximate Bell state of two trapped-ion quantumbits (qubits), independent of their initial states. Compared with previous studies that involved dissipative entanglement of atomic ensembles3 or the application of sequences of multiple timedependent gates to trapped ions4,we implement our combined process using trapped-ion qubits in a continuous time-independent fashion (analogous to optical pumping of atomic states). By continuously driving the system towards the steady state, entanglement is stabilized even in the presence of experimental noise and decoherence. Our demonstration of an entangled steady state of two qubits represents a step towards dissipative state engineering, dissipative quantum computation and dissipative phase transitions5–7. Following this approach, engineered coupling to the environment may be applied to a broad range of experimental systemsto achieve desired quantum dynamics or steady states. Indeed, concurrently with this work, an entangled steady state of two superconducting qubits was demonstrated using dissipation8.