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Oxide double perovskites wherein octahedra formed by both 3d elements and sp-based heavy elements give rise to unconventional magnetic ordering and correlated quantum phenomena crucial for futuristic applications. Here, by carrying out experimental and first principles investigations, we present the electronic structure and magnetic phases of Ba2MnTeO6, where Mn^2+ ions with S = 5/2 spins constitute a perfect triangular lattice. The magnetic susceptibility reveals a large Curie- Weiss temperature -152 K suggesting the presence of strong antiferromagnetic interactions between Mn^2+ moments in the spin lattice. A phase transition at 20 K is revealed by magnetic susceptibility and specific heat which is attributed to the presence of a sizeable inter-plane interactions. Below the transition temperature, the specific heat data show antiferromagnetic magnon excitations with a gap of 1.4 K. Furthermore, muon spin-relaxation reveals the presence of static internal fields in the ordered state and provides strong evidence of short-range spin correlations for T > TN. The DFT+U calculations and spin-dimer analysis infer that Heisenberg interactions govern the inter and intra-layer spin-frustrations in this perovskite. The inter and intra-layer exchange interactions are of comparable strengths (J1 = 4.6 K, J2 = 0.92 J1). However, a weak third nearest-neighbor ferromagnetic inter-layer interaction exists (J3=-0.04 J1) due to double-exchange interaction via the linear path Mn-O-Te-O-Mn. The combined effect of J2 and J3 interactions stabilizes a three dimensional long-range magnetic ordering in this frustrated magnet.