We report the effect of annealing atmosphere on structure and magnetic and dielectric properties of double perovskite-type EuCo_0.5Mn_0.5O₃ (ECMO). Polycrystalline samples prepared by high-temperature reaction were subjected to annealing in different oxygen partial pressures and investigated by powder X-ray diffraction, magnetometry, and ac impedance spectroscopy. While the samples annealed in air or oxygen environment were found to have cation-disordered orthorhombic structure (Pnma), the samples annealed in inert atmosphere have Eu³⁺ deficient perovskite-type structure. The temperature- and field-dependent magnetizations indicate the ferromagnetic transition around 130 K. The differences in field-cooled and zero-fieldcooled magnetization and significant effect of magnetic field on magnetic properties suggest metamagnetic behavior in ECMO. Randomly distributed clusters of ferromagnetically (FM) and antiferromagnetically (AFM) paired magnetic ions and their relative proportions are reflected in their magnetic properties. The weak nature of the antiferromagnetic interactions is reflected in the switching of AFM to FM state at appreciably lower field strength ( ~ 300 Oe). Dielectric measurements indicate that the samples annealed in air or oxygen show large dielectric permittivity (≥2000) compared to that in inert atmosphere ( ~ 400). The analyses of temperature- and frequency-dependent loss tangent and modulus data revealed two different types of relaxations which possibly originate from two polaronic conduction processes.