Berth allocation and pilotage planning are the two most important decisions made by a seaport for serving incoming vessels. Traditionally, the berth allocation problem and the pilotage planning problem are solved sequentially, leading to suboptimal or even infeasible solutions for vessel services. This paper investigates a vessel service planning problem (VSPP) in seaports that addresses berth allocation and pilotage planning in combination. We introduce a compact mixed-integer linear programming formulation for the problem, which can be solved by general-purpose solvers. To solve large-scale instances, we develop an exact solution approach that combines Benders decomposition and column generation in a novel and effective way. Unlike the traditional three-phase Benders decomposition and column generation method, which does not guarantee optimality, we propose a branching scheme that enables the approach to determine an optimal solution to the VSPP. The approach is enhanced through practical acceleration strategies. Extensive computational results using data instances from one of the world's largest seaports show that these acceleration strategies significantly improve the performance of our solution approach and that it can obtain optimal or near-optimal solutions for instances of realistic scale. We perform sensitivity tests to demonstrate the robustness of the approach against variations in problem settings. We also show the benefits brought by integrated optimization by comparing our solution approach with a method that handles berth allocation and pilotage planning sequentially.