We demonstrate that entanglement of two macroscopic nanoelectromechanical resonators ‒ coupled to each other via a common detector, a tunnel junction ‒ can be generated by running a current through the device. We introduce a setup that overcomes generic limitations of proposals suggesting to entangle systems via a shared bath. At the heart of the proposal is an Andreev entangler setup, representing an experimentally feasible way of entangling two nanomechanical oscillators. Instead of relying on the coherence of a (fermionic) bath, in the Andreev entangler setup, a split Cooper pair that coherently tunnels to each oscillator mediates their coupling and thereby induces entanglement between them. Since entanglement is in each instance generated by Markovian and non- Markovian noisy open system dynamics in an out-of-equilibrium situation, we argue that the present scheme also opens up perspectives to observe dissipation-driven entanglement in a condensed-matter system.