Polycrystalline DyxSr2-xTiMnO6 (x = 0, 0.5) double perovskite oxides crystallize in cubic structure (Space group Fm-3m, No. 225) at room temperature. The oxide Sr2TiMnO6 orders antiferromagnetically at ∼14 K (TN) below which zero-field-cooled and field-cooled magnetization data show bifurcation. Magnetization of the sample Dy0.5Sr1.5TiMnO6 shows only a tendency to order around 3 K and no clear signature of magnetic ordering. The magnetization value at 2 K is greatly enhanced in the Dy-substituted sample compared to that in parent Sr2TiMnO6. The real part of the dielectric permittivity of both DyxSr2-xTiMnO6 (x = 0, 0.5) oxides are of the order of 104 at room temperature. The colossal dielectric constant values in these oxides could be understood in terms of intrinsic hopping conduction and extrinsic Maxwell-Wagner relaxation mechanism. Powder x-ray diffraction data confirm that Sr2TiMnO6 does not undergo any structural transition in the temperature range of 300 K to 800 K and reveal normal thermal expansion behaviour. X-ray photoelectron spectroscopy data on Dy0.5Sr1.5TiMnO6 indeed confirm the presence of mixed valence states for Mn (Mn3+ and Mn4+) as expected from magnetization measurements. Thus rare earth ion substitution at Sr-site of Sr2TiMnO6 is a sensitive method to tune the magnetic properties while preserving the colossal dielectric property. © 2018 IOP Publishing Ltd.