We explored the electronic and magnetic properties of the lanthanide double perovskite Dy2FeCoO6 by combining magnetization, Raman and Mössbauer spectroscopy and neutron diffraction along with density functional theory (DFT) calculations. Our magnetization measurements revealed two magnetic phase transitions in Dy2FeCoO6. First, a paramagnetic to antiferromagnetic transition at T
N = 248 K and subsequently, a spin reorientation transition at T
SR = 86 K. In addition, a field-induced magnetic phase transition with a critical field of H
c ≈ 20 kOe is seen at 2 K. Neutron diffraction data suggested cation-disordered orthorhombic structure for Dy2FeCoO6 in Pnma space group which is supported by Raman scattering results. The magnetic structures ascertained through representational analysis indicate that at T
N, a paramagnetic state is transformed to Γ5(Cx, Fy, Az) antiferromagnetic structure while, at T
SR, Fe/Co moments undergo a spin reorientation to Γ3(Gx, Ay, Fz). The refined magnetic moment of (Fe/Co) is 1.47(4) μ
B at 7 K. The antiferromagnetic structure found experimentally is supported through the DFT calculations which predict an insulating electronic state in Dy2FeCoO6.