Grapevine roots, as a side-stream of a vineyard, are a sustainable resource for the recovery of oligomeric stilbenoids, such as the bioactive r-viniferin. The aim of this study is to evaluate an in silico-supported method, based on the Conductor-like Screening Model for Real Solvents (COSMO-RS), for selection of environmentally friendly natural deep eutectic solvents (NADES) with regard to the extraction of grapevine roots. The most suitable NADES system for ultrasonic-assisted extraction of r-viniferin was choline chloride/1,2-propanediol. The optimal extraction parameters for r-viniferin were determined using single-factor experiments as follows: choline chloride/1,2-propanediol 1/2 mol/mol, 10 wt% H2O, biomass/NADES ratio 1/10 g/g, and 10 min extraction time. Under optimized conditions, the extraction yield of r-viniferin from grapevine roots reached 76% of the total r-viniferin content. Regarding stability, stilbenoids in choline chloride/1,2-propanediol remained stable during 128 days of storage at ambient temperature. However, fructose/lactic acid-based NADES were observed to degrade stilbenoids; therefore, the removal of the NADES will be of interest, with a suitable method implemented using Amberlite® XAD-16N resin. As green solvents, the NADES have been used as effective and environmentally friendly extractants of stilbenoid-containing extracts from grapevine roots for potential applications in the cosmetic and pharmaceutical industry or as nutraceuticals in the food industry.