A water-free, ternary solvent mixture consisting of a natural deep eutectic solvent (NADES), ethanol, and triacetin was investigated concerning its ability to dissolve and extract curcumin from Curcuma longa L. To this purpose, 11 NADES based on choline chloride, acetylcholine, and proline were screened using UV–vis measurements. A ternary phase diagram with a particularly promising NADES, based on choline chloride and levulinic acid was recorded and the solubility domains of the monophasic region were examined and correlated with the system’s structuring via light scattering experiments. At the optimum composition, close to the critical point, the solubility of curcumin could be enhanced by a factor of >1.5 with respect to acetone. In extraction experiments, conducted at the points of highest solubility and evaluated via HPLC, a total yield of ~84% curcuminoids per rhizome could be reached. Through multiple extraction cycles, reusing the extraction solvent, an enrichment of curcuminoids could be achieved while altering the solution. When counteracting the solvent change, even higher concentrated extracts can be obtained.