Appropriate waste and resource management are essential for a sustainable circular economy with reduced environmental impact. With critical resources, e-waste may serve as indirect raw material. For example, with NdFeB permanent magnets, Neodymium (Nd) and the co-present Dysprosium (Dy) are critical rare earth elements (REEs). However, there exists no economically viable technology for recycling them from electronic waste (e-waste). Here, a method is presented based on cloud point extraction (CPE). The work involves basic complexation chemistry in a cloud medium with pure REE salts, as well as, with real NdFeB-magnets (nearly 28% REE content by weight) from an old hard disk drive (5.2 g magnet in a 375 g HDD). High extraction efficiency (>95%) was achieved for each REE targeted (Nd, Dy, Praseodymium (Pr)). With the magnet waste, the cloud phase did hardly contain any Nickel (Ni), Cobalt (Co), or Boron (B), but some Aluminium (Al) and Iron (Fe). Dynamic light scattering results indicated aggregation of ligand-surfactant micelles with the cloud phase. The preconcentrated products can be used for new Nd magnet manufacturing or further enriched using established transition metal removal techniques. Reuse of solvent, low chemical inventory demand, and using non-inflammable, non-volatile organic extractants promise safe large-scale operation, low process costs, and less environmental impact than using hydrometallurgical methods used with urban or primary mining.