Autonomous underwater vehicle (AUV) docking and wave energy converters (WECs) have been investigated thoroughly over past decades. Separate development of these technologies in the past few years by the authors are being brought together to propose an underwater docking system for a WEC-based mobile station. This paper presents the concept of WEC-based offshore AUV residency and reports the development of the proposed system. A finite-horizon model predictive control approach is presented to demonstrate the feasibility of “rendezvous” style docking of a box-type AUV to a simulated WEC experiencing sinusoidal vertical oscillations. It is found that the AUV tends to approach the dock when its oscillatory velocity approaches zero.