Autonomous Mobility-on-Demand (AMoD) systems are a rapidly evolving mode of transportation in which a centrally coordinated fleet of self-driving vehicles dynamically serves travel requests. The control of these systems is typically formulated as a large network optimization problem, and reinforcement learning (RL) has recently emerged as a promising approach to solve the open challenges in this space. However, current RL-based approaches exclusively focus on learning from online data, fundamentally ignoring the per-sample-cost of interactions within real-world transportation systems. To address these limitations, we propose to formalize the control of AMoD systems through the lens of offline reinforcement learning and learn effective control strategies via solely offline data, thus readily available to current mobility operators. We further investigate design decisions and provide experiments on real-world mobility systems showing how offline learning allows to recover AMoD control policies that (i) exhibit performance on par with online methods, (ii) drastically improve data efficiency, and (iii) completely eliminate the need for complex simulated environments. Crucially, this paper demonstrates that offline reinforcement learning is a promising paradigm for the application of RL-based solutions within economically-critical systems, such as mobility systems.