Grid integration of wave energy involves various power train stages from device to grid, such as a power take-off stage, a power conversion stage, and a power conditioning stage. The coupled performance of the complete wave-to-grid system depends heavily on the dynamics of each stage and their respective controllers. However, the control objectives of various stages may not align with each other and pose a potential problem, in terms of economic performance and grid integration. This study presents a complete wave-to-grid control approach for a wave energy converter, ensuring that the system performs optimally under variable wave resource conditions. The proposed system comprises a point absorber wave energy converter oscillating in heave, a linear permanent magnet generator, and back-to-back power converters for connection to the grid. Additionally, short term energy storage, based on an ultra-capacitor, is also added to the DC link between the back-to-back converters for power quality improvement. In the paper, a mathematical model is derived for the individual components of the wave-to-grid system. Then, the controllers for each stage of the power train are designed. A LiTe-Con controller is used for maximum power extraction on the device side, while Lyapunov-based nonlinear controllers are designed for power converter control in order to achieve the full range of control objectives. The result shows that the proposed controllers accomplish the desired control objectives and perform well under various operating conditions.