The IC lead frame is an essential component in semiconductor packaging, primarily composed of a nickel (Ni)–copper (Cu) alloy in which Ni is electroplated onto a Cu substrate. In this study, synergistic solvent extraction using a binary extractant containing LIX984N and Cyanex302, followed by two-stage selective stripping using sulfuric acid (H2SO4) and nitric acid (HNO3) as the stripping agent, was employed to separate and recover Cu and Ni from the leachate of an IC lead frame. The results indicated that under the optimal conditions of synergistic solvent extraction with an extraction pH value of 1, an extractant concentration of 0.015 M LIX984N + 0.0375 M Cyanex302, an extraction aqueous/organic (A/O) ratio of 1:1, and an extraction time of 5 min, the extraction efficiencies for Cu and Ni were 99.8% and 1.17%, respectively. The distribution ratios were DCu 999 and DNi 0.012, resulting in a separation factor of 83,250. In addition, the separation factor was much higher than that of using individual extractant of LIX984N (6208.3) or Cyanex302 (22,185.2). Subsequently, under optimal first-stage stripping conditions, using 0.05 M H2SO4 at a stripping organic/aqueous (O/A) ratio of 1:1, and with a stripping time of 3 min, a stripping efficiency of 99.9% for Ni was achieved. Next, under optimal second-stage stripping conditions, using 5 M HNO3 at a stripping O/A ratio of 2:1, and with a striping time of 3 min, a stripping efficiency of 99.9% for Cu was achieved. Finally, sodium hydroxide (NaOH) was added to the respective stripping solutions to precipitate Ni and Cu ions, followed by calcination treatment for the precipitates to obtain NiO and CuO, respectively. The purity of the former was 99.74% and that of the latter was 99.82%. The results demonstrate that synergistic solvent extraction using a binary extractant containing LIX984N and Cyanex302 can almost entirely extract Cu in the leachate of an IC lead frame at a lower extraction pH and a lower extractant concentration, thus reducing the co-extraction of Ni. In addition, less co-extracted Ni in the organic phase can be selectively stripped using dilute H2SO4, thus reducing the co-stripping of Cu. Hence, the effective separation and recovery of Cu and Ni in IC lead frame leachate can be achieved, which contributes to improving the sustainability of natural resources.