This article presents the development of a Fuzzy Guidance System (FGS) for unmanned aerial vehicles capable of pursuing and performing rendezvous with static and mobile targets. The system is designed to allow the vehicle to approach a maneuvering target from a desired direction of arrival and to terminate the rendezvous at a constant distance from the target. In order to perform a rendezvous with a maneuvering target, the desired direction of arrival is adjusted over time to always approach the target from behind, so that the aircraft and target velocity vectors become aligned. The proposed guidance system assumes the presence of an autopilot and uses a set of Takagi-Sugeno fuzzy controllers to generate the orientation and speed references for the velocity and heading control loops given the relative position and velocity between the aircraft and the target. The FGS treats the target as a mobile waypoint in a 4-D space (position in 2-dimensions, desired crossing heading and speed) and guides the aircraft on suitable trajectories towards the target. Only when the vehicle is close enough to the rendezvous point, the guidance law is complemented with an additional linear controller to manage the terminal formation keeping phase. The capabilities of the proposed Rendezvous-FGS are verified in simulation on both maneuvering and non-maneuvering targets. Finally experimental results using a multi-rotor aerial system are presented for both fixed and accelerating targets.