In this study, gearbox radiated noise was successfully reduced through housing shape optimization. First, dynamic and structural–acoustic coupled analysis models of an agricultural UTV gearbox were developed. Then, the test equipment was configured to match that of the simulation model, and a test was conducted. The analysis and test results showed errors within 0.1 dB for vibration and 0.2 dB(A) for noise, indicating that the models were reliable. The housing design was then optimized using topology optimization based on the developed structural–acoustic coupling analysis model. The sound pressure level around the housing was used as an objective function for topology optimization. The optimal distribution of materials for the housing was also derived to reduce the radiated noise. Lastly, the housing rib was designed based on the optimization result, and an improvement in the radiated noise by approximately 2.43 dB(A) was confirmed in the operation area.