Extra virgin olive oil (EVOO) from Olea europaea L. drupes, a cornerstone in the Mediterranean diet, is well known for its nutritional and health properties, especially for prevention of cardiovascular diseases and metabolic disorders. Traditionally, beneficial health effects have been largely attributed to the high concentration of monounsaturated fatty acids, and in recent years, these have also been related to other components including oleacein and oleocanthal. Here, we evaluated, for the first time, the antimicrobial activity of different green extra virgin olive oil-based formulations in natural deep eutectic solvents (NaDESs) emerging as powerful and biocompatible solvents. Specifically, the antimicrobial activity of the EVOO extract, as well as purified oleocanthal and oleacein in two NaDESs (choline/glycerol and choline/propylene glycol), against several drug-resistant clinical isolates and standard microbial strains has been evaluated. The main result was the inhibitory activity of the EVOO extract in choline/glycerol as well as oleacein in choline/propylene glycol toward drug-resistant Gram-positive and -negative strains. Specifically, the EVOO extract in choline/glycerol showed the highest antibacterial activity against several clinical strains of Staphylococcus aureus, whereas oleacein in choline/propylene glycol was the most effective toward various clinical strains of Escherichia coli, Pseudomonas aeruginosa, and Klebsiella pneumoniae. In addition, all the formulations tested were effective against Candida spp. In conclusion, our results suggest EVOO-based formulations in NaDESs as an interesting strategy that may help in reducing the risk of development of drug resistance. Under this perspective, the usage of NaDESs for the preparation of new antimicrobial formulations may represent a promising approach.