This paper presents an attitude regulation controller that is utilized by a nanosatellite, called Deorbiter CubeSat, intended for the removal of sizable debris from low Earth orbit. The controller is used to detumble an uncooperative debris object to which the Deorbiter CubeSat is attached. The spacecraft performs a rendezvous maneuver, attaches rigidly to the exterior of the target debris, and detumbles and steers it toward the deorbit altitude. Three reaction wheels, in a mutually-orthogonal configuration, are used to control the attitude of the combined CubeSat and debris system. Each reaction wheel is capable of producing about 20 mN·m of torque, and has a maximum momentum capacity of 60 mN·m·s. Since physical parameters of the debris to be detumbled, e.g., mass and moment of inertia, are not known a priori, or there are large uncertainties in their values, the detumbling controller estimates the unknown parameters in order to reduce the regulation error to zero over time. Simulation results show that the controller is able to fully detumble the CubeSat-debris system in a matter of minutes, without knowing the debris physical parameters in the beginning of the maneuver.