We theoretically investigate the dynamics of two spin qubits interacting with a magnetic medium. A systematic theoretical framework for this qubit-magnet hybrid system is developed in terms of the equilibrium properties of the magnetic medium. Our particular focus is on the induced dissipative coupling between the spin qubits. In contrast to the conventional wisdom that dissipation is detrimental to quantum effects, here we show that a sizable long-lifetime entanglement can be established via a dissipative environment, in the absence of any coherent coupling. Moreover, we demonstrate that maximally-entangled two-qubit states (Bell states) can be achieved in this scheme when complemented by proper postselection. In this situation, there is a dynamical phase transition separated by an exceptional point. The resultant Bell state is robust against weak random perturbations and does not require the preparation of a particular initial state. Our study may find applications in quantum information science, quantum spintronics, and for sensing of nonlocal quantum correlations.