Double perovskites have been extensively studied in materials chemistry due to their excellent properties and novel features attributed to the coexistence of ferro/ferri/antiferro-magnetic ground state and semiconductor band gap within the same material. Double perovskites with Sr2NiMO6 (M = Te, W) structure type have been synthesized using simple, non-toxic and costless aqueous citrate sol-gel route. The reaction yielded phase-pure nanocrystalline powders of two compounds: Sr2NiWO6 (SNWO) and Sr2NiTeO6 (SNTO). According to the Rietveld refinement of powder X-ray diffraction data at room temperature, Sr2NiWO6 is tetragonal (I4/m) and Sr2NiTeO6 is monoclinic (C12/m1), with average crystallite sizes of 49 and 77 nm, respectively. Structural studies have been additionally performed by Raman spectroscopy revealing optical phonons typical for vibrations of Te6+/W6+O6 octahedra. Both SNTO and SNWO possess high values of dielectric constants (341 and 308, respectively) with low dielectric loss (0.06 for SNWO) at a frequency of 1 kHz. These values decrease exponentially with the increase of frequency to 1000 kHz, with the dielectric constant being around 260 for both compounds and dielectric loss being 0.01 for SNWO and 0.04 for SNTO. The Nyquist plot for both samples confirms the non-Debye type of relaxation behavior and the dominance of shorter-range movement of charge carriers. Magnetic studies of both compounds revealed antiferromagnetic behavior, with Néel temperature (TN) being 57 K for SNWO and 35 K for SNTO.