Quantum feedback control enables the stabilization of non-equilibrium states of a quantum system in the presence of decoherence-induced errors. Measurement-based feedback is the conventional approach, but requires a complicated external feedback loop to correct errors. We describe a simpler implementation, based on autonomous-feedback, to stabilize an entangled state of two transmon qubits. The scheme combines continuous microwave drives with a specifically engineered coupling between the two-qubit register and a dissipative reservoir to force the qubits into a Bell state. Such autonomous schemes, which counterintuitively use dissipation to fight decoherence, will be an essential tool for the implementation of quantum error-correction of a logical qubit.