Monitoring marine areas has become a fundamental activity for addressing key challenges such as biodiversity research and conservation, civilian operations on infrastructures and Marine Protected Areas (MPA), and military surveillance, with a particular focus on Anti-Submarine Warfare (ASW) and the protection of critical infrastructures. A current open problem in these scenarios is the tracking of acoustic sources using passive sonar systems. These systems are characterized by silent operation, i.e., without emitting active pulses, and long endurance, making them suitable for continuous and covert monitoring. Detecting and tracking acoustic sources using Passive Acoustic Monitoring (PAM) sensors is a challenging task that requires deploying many sensors to ensure observability of the acoustic source of interest, significantly increasing the cost and effort of maintenance. To overcome these limitations, this thesis investigates the use of Autonomous Underwater Vehicles (AUVs) to build an Underwater Mobile Sensors Network (UWMSN), where the AUVs act as mobile nodes of a distributed, autonomous passive sonar system. The integration of AUVs introduces new challenges, particularly due to the reliance on underwater acoustic communication, which is subject to latencies, low bandwidth, and packet loss. This work addresses these issues by designing distributed control strategies that allow a team of AUVs to track underwater acoustic targets cooperatively. Because the motion of the sensors directly impacts the performance of the tracking algorithm, a cooperative motion planning strategy based on a Partially Observable Markov Decision Process (POMDP) is proposed. To handle the associated computational complexity, a Model Predictive Control (MPC) scheme is used, enabling online optimization over a moving time horizon. A sequential multi-agent decision-making framework ensures that planning remains fully distributed, avoiding the need for a centralized coordinating node and eliminating single points of failure. The proposed strategy is validated through extensive simulations of complex acoustic monitoring scenarios and supported by a real-world proof of concept. Results demonstrate the effectiveness and robustness of the system in improving tracking performance, reducing system costs, and ensuring resilience against communication constraints, AUV failures, and environmental variability.