In this paper, we investigate the design of an integrated system consisting of two non-rigidly connected bodies: A floating buoy and an emerged offshore structure. When waves excite the buoy to oscillate, the relative motion between the two bodies are converted to useful energy through a spring damper system, resulting in wave energy being absorbed. The parameter to design includes the mass and underwater shape of the buoy. The spring stiffness of the power take-off (PTO) system is constrained to be non-negative with the concerns of complexity in implementation and system stability. Results suggest that a larger mass of the buoy is advantageous due to smaller optimal spring stiffness and damping coefficient of the PTO system, more absorbed wave power, and less motion amplitude of the two bodies. A favorable underwater shape of the buoy is characterized by large diameter to draft ratio, with the section profile preferring a circle or square rather than an equilateral triangle. Investigations on the designed buoy in irregular waves show that the integrated system presents its peak power absorption within the common range of energy period, and the motion amplitude of the offshore structure is larger than the wave amplitude in a certain range of sea states.