The worldwide production of NdFeB magnets has outpaced all other types of magnets owing to their low cost and enhanced magnetic properties. The critical elements required for the production of these magnets are Nd, Pr, and Dy along with other metals. However, the rare earth elements (REEs) come with substantial supply risk. Recycling of REEs from obsolete NdFeB may be a promising alternative to address the supply chain pressure. The purpose of this work is to optimize the water leaching process for the selective recovery of Nd, Pr, Co, and Al from chloride-roasted waste NdFeB magnets, using a statistical approach, and to simultaneously study the effect of significant process variables on the extraction of metals from end-of-life (EOL) magnets. Process optimization was carried out by performing a minimum number of bench scale operations specifically designed for leaching experiments. It was observed that the temperature, time, and pulp density were the most significant process parameters. Tuning of operational parameters was carried out, and model equations were generated for all the response variables with the help of Design Expert software. The response surface methodology (RSM) was used to generate optimized conditions for the leaching process (temperature: 95 °C; pulp density: 100 g/L; time: 60 min), which were further validated by repeating the leaching experiments in triplicate. The extraction efficiency of metal ions was found to be maximum under the optimized leaching conditions.