Deep eutectic solvents (DESs) potential for the extraction of polyphenolic compounds (PC) from mango by-products (peel and seed) was evaluated. Ultrasound (US) and agitation were applied to evaluate the effects of solvent and extraction methodology. The extracts were characterized with antioxidant capacity and HPLC-DAD profile. A theoretical study was performed using density functional theory and the QTAIM approach. β-alanine and choline chloride based DESs were effective to extract PC from peel and seed. Some DES increased PC extraction up to three times for peel (23.05 ± 1.22 mg/g DW) and up to five time for seeds (60.01 ± 1.40 mg/g DW). The PC profile varied with the solvent (DES vs EtOH/MeOH), procedure (US vs agitation) and material (peel or seed). Mangiferin extraction from peels was significantly increased with β-alanine based DES (676.08 ± 20.34 μg/gDW). The strength of H-bonds had a determining effect on the viscosity of DESs. The solute-solvent solvation energy was suitable to estimate the strength of H-bond interactions between DES and target compounds. This study demonstrates the remarkable capacity of DESs to extract PC from mango by-products and provides insights into the factors controlling extraction properties.