This paper studies the problem of localization and tracking of a mobile target ship with an autonomous underwater vehicle (AUV). A hybrid acoustic-optical underwater communication solution is proposed, in which the acoustic link is used for the non-line-of-sight (NLoS) localization, and the optical link is for the line-of-sight (LoS) transmission. By coordinating these two complementary technologies, it is possible to overcome their respective weaknesses and achieve accurate localization, tracking, and high-rate underwater data transmission. The main challenge for reliable operation is to maintain the AUV over an optical link range while the target dynamics is unknown at all times. Hence, we design an error-based adaptive model predictive controller (MPC) and a proportional-derivative (PD) controller incorporating a real-time acoustic localization system to guide the AUV towards the sensor node mounted on the surface ship. We define a connectivity threshold cone with its apex coinciding with the sensor node such that when the underwater vehicle stays inside of this cone, a minimum bit rate is guaranteed. The localization, tracking control and optical communication scheme are validated through online simulations that integrate a realistic AUV model where the effectiveness of the proposed adaptive MPC and PD controller are demonstrated.