Over the past decades the steep increase in the number of space-debris objects have sparked many studies into active space-debris removal. Past collisions have shown that space debris is a very real threat to operational satellites and active debris removal is necessary to stabilize the situation. ESA has, therefore, performed multiple studies on the removal of the no longer operational satellite ENVISAT from orbit. Since ENVISAT lost functionality, it has acquired a tumbling motion, which poses many challenges for a removal mission. A scenario was proposed in which a chaser spacecraft performs a rendezvous with ENVISAT, to actively de-orbit the satellite. To increase the robustness to unexpected events and reduce operational costs it is highly desirable that these operations can be performed autonomously. In this research an autonomous guidance and orbit control system was developed that enables the final phase of the rendezvous with ENVISAT. An approach strategy was adopted that aims to maintain alignment with the spin axis of ENVISAT throughout the approach. The designed algorithms use convex guidance to ensure globally-optimal solutions, while at the same time constraining the trajectory. The guidance algorithm minimizes a weighed combination of the thrust and the state error. Furthermore, the concept of model predictive control is applied to allow for an unconstrained time-to-go. Two guidance and control strategies were examined in this research, one that is solely based on model predictive control and another that employs an additional LQR-controller. The functional simulations were complemented by hardware-in-the-loop simulations using the DLR flat-floor test facility, TEAMS. These real-time tests also include the docking phase. Both the functional and hardware-in-the-loop simulation results show that the baseline model predictive control method can successfully perform the operations with an accuracy well above the requirement. It was found that implementing an extra LQR controller resulted in a similar accuracy, but an increase in mission propellant of 21%. The functional simulation results also revealed that the required mission propellant, compared to the baseline, could be decreased further by 18%, while maintaining the baseline accuracy. This is achieved by optimizing the weight parameters used in the convex optimization. It does, however, lead to an increased mission duration. The designed algorithms were successfully implemented on TEAMS, where it was shown that the addition of an LQR controller again leads to a higher use of propellant and on top of that it results in a longer operation time.