Electric propulsion is currently seen as a key enabling technology for space debris removal missions aimed at deorbiting multiple debris targets. This paper develops an autonomous onboard orbit control strategy tailored to these missions. The control problem is divided into four stages, involving a sequence of low-thrust orbital transfer and rendezvous maneuvers. A feedback control law is derived for each maneuvering stage, by exploiting Lyapunov-based and model predictive control techniques. The proposed design is able to account for mission-specific performance and safety requirements, while satisfying on–off constraints inherent to the propulsion technology. Simulation case studies of a multidebris removal mission demonstrate the effectiveness of the proposed control strategy, and support the viability of electric propulsion for such type of missions.