The presence of valuable and hazardous metals in waste printed circuit boards, especially, motherboards, makes their recovery necessary as implies great economic and environmental advantages and develops urban mining processes. Hence, this research is focused on the selective leaching of Cu, Pb, and Sn as base metals using nitric acid and hydrochloric acid and Au, Ag, and Pd as precious metals using thiourea and sodium thiosulfate from waste motherboards’ PCBs in a sequential eco-friendly two-stage process. Previously, thiourea and sodium thiosulfate were used as leaching agents to investigate their applicability for the leaching of metals from PCBs in a single-stage process. Screening experimental design was applied to screen the variables affecting the leaching process in order to evaluate their impact on the recovery of metals and select the significant factors. The results demonstrated that base and precious metals can be leached appropriately in two consecutive stages compared to a single-stage process. Nitric acid was found to be a much more efficient agent to leach Cu and Pb in comparison with hydrochloric acid which was more suitable for the leaching of Sn. In the case of precious metals, higher amounts of Au were leached using thiourea, whereas sodium thiosulfate was able to leach more Pd. Roughly similar results were obtained for the leaching of Ag using these leaching agents. Nitric acid concentration, average particle size, temperature, and leaching time were found to be significant to maximize the leaching of Cu and Pb and minimize that for Au, Ag, and Pd in the first stage. Initial pH was the only variable influencing the second stage, in particular, Au leaching by thiourea.