This paper presents a neural operator-based approach to solving optimal control problems for subsurface reservoir systems. Reservoirs are complex distributed-parameter systems governed by partial differential equations (PDEs). Conventional approaches that solve the governing equations numerically provide high-fidelity simulations of transient flow in porous media but are computationally intensive: for many scenarios, runtimes reach hours even on high-performance computing (HPC) clusters. Consequently, computational efficiency is a key bottleneck for deploying numerical reservoir simulators in decision support and optimal control. Modern deep learning methods—specifically, neural operators trained on reservoir simulation data—offer a fast and effective alternative for approximating PDE solution operators. Owing to their differentiable structure, neural operators support automatic differentiation of objective functionals, enabling gradient-based optimization with substantially reduced computational cost. The main contributions are a theoretical upper bound on the control error that depends explicitly on properties of the neural operator, and the development of an optimal control method within the proposed framework. Practical relevance and high computational efficiency are demonstrated on a reservoir well-control optimization problem, illustrating the method’s applicability to real-field settings that demand fast evaluation of operational strategies and consistent enforcement of production constraints.