Chelating agents’ application for EOR and well stimulation is fast growing nowadays. However, reagents of this class have some drawbacks, with high values of interfacial tension (IFT) being among them. IFT may be lowered with the addition of surfactants; however, the simultaneous application of chelating agents and surfactants has not yet been widely studied. This paper focuses on the experimental and theoretical investigation of the interaction between chelating agent (ethylenediaminetetraacetic acid, EDTA) and surfactants of anionic and cationic types (sodium dodecyl sulfate, SDS, and dodecyl trimethynlammonium bromide, DTAB). IFT measurement was performed at ambient conditions, with normal octane being as the reference hydrocarbon to eliminate the temperature and salinity effects and compare surfactant-containing systems. The experimental results show that chelating agents’ addition to the solutions of surfactants leads to a decrease in IFT value. Moreover, surfactants’ critical micelle concentration is lowered, whereas their effectiveness and efficiency are increased, which points to the salting-out nature of chelating agents. Molecular dynamics reveal that chelating agent addition causes closer packing of surfactant layer, the decrease in head groups’ hydration, and, at least in the case of SDS, specific surfactant–chelating agent attractive interaction. These molecular-level insights, experimental dependencies, and the combined methodology may be useful for the proper selection of fluids for real-field operations.