Borage flower (Echium amoenum), an annual herb native to the Mediterranean region, is an excellent source of anthocyanins and is widely used in various forms due to its biological activities. In the present study, a choline chloride and glycerol (CHGLY)-based natural deep eutectic solvent (NADES) was applied in order to extract the anthocyanins from borage flowers. The traditional solvents, including water, methanol, and ethanol, were used to evaluate the efficiency of CHGLY. The results showed that CHGLY was highly efficient compared to the traditional solvents, providing the highest amounts of the total anthocyanin content (TAC), total phenolic content (TPC), total flavonoid content (TFC), individual anthocyanins, and antioxidant activity (DPPH radical scavenging (DPPH) and ferric-reducing antioxidant power (FRAP) assays). The most dominant anthocyanin found in studied borage was cyanidin-3-glucoside, followed by cyanin chloride, cyanidin-3-rutinoside, and pelargonidin-3-glucoside. The bioavailability % was 71.86 ± 0.47%, 77.29 ± 0.57%, 80.22 ± 0.65%, and 90.95 ± 1.01% for cyanidin-3-glucoside, cyanidin-3-rutinoside, by pelargonidin-3-glucoside and cyanin chloride, respectively. However, cyanidin-3-glucoside was the anthocyanin compound showing the highest stability (99.11 ± 1.66%) in the gastrointestinal environment. These results suggested that choline chloride and glycerol-based NADES is not only an efficient, eco-friendly solvent for the extraction of anthocyanins but can also be used to increase the bioavailability of anthocyanins.