As the negative impact of man-made underwater radiated noise (URN) on marine life is recognized by the scientific community, guidelines and initiatives are proposed by port authorities and international organizations for monitoring and reducing URN from ship operations. In medium to large-size ships, propellers are often the dominating URN source as compared to on board machinery and flow turbulence. Within this paper, URN from cavitating flow around a ship propeller in behind-hull condition is predicted by a high-fidelity CFD solver, coupled with an acoustic analogy method. The noise sources are hydrodynamic flow fields around propeller and rudder models, simulated by CFD with a multi-phase flow model. Far-field acoustic noise is calculated by the permeable Ffowcs-Williams Hawkings (FWH) acoustic analogy method. Unsteady cavitation patterns and URN levels from the numerical predictions are validated against experimental results from a cavitation tunnel test. The propeller blade shape is optimized for minimum cavity volume by parametric design variations and performance evaluations based on steady CFD simulations with a simplified hull wake model. The URN predictions from unsteady CFD-FWH simulations demonstrate that the cavity volume reduction for the optimized blade design can lead to considerable decrease of low-frequency tonal noise.