The recycling of metals from waste printed circuit boards (WPCBs) has been presented as a solid–liquid extraction process using two deep eutectic solvents (DESs) and four ionic liquids (ILs). The extraction and separation of Cu(II), Ag(I), and other metals, such as Al(III), Fe(II), and Zn(II), from the solid WPCBs (after the physical, mechanical, and thermal pre-treatments) with different solvents are demonstrated. Two popular DESs were used to recover valuable metal ions: (1) choline chloride + malonic acid, 1:1, and (2) choline chloride + ethylene glycol, 1:2. The extraction efficiencies of DES 1 after two extraction and two stripping stages were only 15.7 wt% for Cu(II) and 17.6 wt% for Ag(I). The obtained results were compared with those obtained with four newly synthetized ILs as follows: didecyldimethylammonium propionate ([N10,10,1,1][C2H5COO]), didecylmethylammonium hydrogen sulphate ([N10,10,1,H][HSO4]), didecyldimethylammonium dihydrogen phosphate ([N10,10,1,1][H2PO4]), and tetrabutylphosphonium dihydrogen phosphate ([P4,4,4,4][H2PO4]). Various additives, such as didecyldimethyl ammonium chloride surfactant, DDACl; hydrogen peroxide, H2O2; trichloroisocyanuric acid, TCCA; and glycine or pentapotassium bis(peroxymonosulphate) bis(sulphate), PHM, were used with ILs during the extraction process. The solvent concentration, quantity of additivities, extraction temperature, pH, and solid/liquid, as well as organic/water ratios, and the selectivity and distribution ratios were described for all of the systems. The utilization of DESs and the new ILs with different additives presented in this work can serve as potential alternative extractants. This will help to compare these extractants, additives, extraction efficiency, temperature, and time of extraction with those of others with different formulas and procedures. The metal ion content in aqueous and stripped organic solutions was determined by the ICP-MS or ICP-OES methods. The obtained results all show that solvent extraction can successfully replace traditional hydrometallurgical and pyrometallurgical methods in new technologies for the extraction of metal ions from a secondary electronic waste, WPCBs.