Context: The Galactic H ii region NGC 2579 has stayed undeservedly unexplored due to identification problems which persisted until recently. Both NGC 2579 and its companion ESO 370-9 have been misclassified as planetary or reflection nebula, confused with each other and with other objects. Due to its high surface brightness, high excitation, angular size of few arcminutes and relatively low interstellar extinction, NGC 2579 is an ideal object for investigations in the optical range. Located in the outer Galaxy, NGC 2579 is an excellent object for studying the Galactic chemical abundance gradients. Aims: To present the first comprehensive observational study on the nebular and stellar properties of NGC 2579 and ESO 370-9, including the determination of electron temperature, density structure, chemical composition, kinematics, distance, and the identification and spectral classification of the ionizing stars, and to discuss the nature of ESO 370-9. Methods: Long slit spectrophotometric data in the optical range were used to derive the nebular electron temperature, density and chemical abundances and for the spectral classification of the ionizing star candidates. Hα and UBV CCD photometry was carried out to derive stellar distances from spectroscopic parallax and to measure the ionizing photon flux. Results: The chemical abundances of He, N, O, Ne, S, Cl, and Ar were obtained. Maps of electron density and radial velocity with a spatial resolution of 5" × 5" were composed from long slit spectra taken at different declinations. Three O stars classified as O5 V, O6.5 V, and O8 V were found responsible for the ionization of NGC 2579, while ESO 370-9 is ionized by a single O8.5 V star. The estimated mass of ionized gas of ≈25 M_&sun; indicates that ESO 370-9 is not a planetary nebula, but a small H ii region. A photometric distance of 7.6 ± 0.9 kpc and a kinematic distance of 7.4 ± 1.4 kpc were obtained for both objects. At the galactocentric distance of 12.8 ± 0.7 kpc, NGC 2579 is one of the most distant Galactic H ii regions for which direct abundance determinations have been accomplished.