Wire and arc additive manufacturing (WAAM) is among the most promising additive manufacturing techniques for metals because it yields high productivity at low raw material costs. However, additional post-processing is required to remove redundant surface material from components manufactured by the WAAM process, and thus the productivity decreases. To increase productivity, multi-variable process parameters need to be optimized, including thermo-mechanical effects caused by high deposition rates. When the process is modeled, deposit shape and productivity are challenging to quantify due to uncertainty in multiple variables of the complicated WAAM process. Therefore, we modeled the WAAM process parameters, including uncertainties, using a Gaussian process regression (GPR) method, thus allowing us to develop a WAAM optimization model to improve both productivity and the quality of the deposit shape. The accuracy of the optimized output was verified through a close agreement with experimental values. The optimized deposited material had a wide effective area ratio, small height differences, and near 90° deposition angle, highlighting the usefulness of the GPR model approach to deposit nearly ideal material shapes.