Online approximation of the optimal station-keeping strategy for a marine craft subject to an irrotational current is considered. An approximate policy that minimizes a user-defined cost function over an infinite time horizon is obtained using an actor-critic-identifier-based adaptive dynamic programming technique. The hydrodynamic drift dynamics are assumed to be unknown; therefore, a concurrent learning-based system identifier is developed to identify the unknown model parameters. The identified model is used to implement an adaptive model-based reinforcement learning technique to estimate the unknown value function. The developed policy guarantees uniformly ultimately bounded convergence of the vehicle to the desired station and uniformly ultimately bounded convergence of the approximated policies to the optimal polices without the requirement of persistence of excitation. The developed strategy is validated using an autonomous underwater vehicle, where the three degrees-of-freedom in the horizontal plane are regulated. The experiments are conducted in a second-magnitude spring located in central Florida.