We present single-crystal growth and magnetic property studies of tellurium-bridged copper spin-12 system Ba2CuTeO6. The spin-exchange interaction among copper spins via Cu-O-Te-O-Cu super-superexchange route leads to a novel two-leg spin ladder system. Spin susceptibility χ(T) data indicate that the triclinic Ba2CuTeO6 undergoes a stepwise crossover for exchange couplings revealed by a broad maximum of χ(T) near Tmax∼75 K and an anisotropic cusp in dχdT(T) at TN∼15 K to signify a three-dimensional (3D) antiferromagnetic long-range ordering (LRO). The 3D LRO has been suggested from the anisotropic behavior of χ(T) with strong c-axis spin anisotropy and the signature of spin-flop transition from the isothermal magnetization below TN. Analysis of magnetic heat capacity (Cm) at TN∼15 K indicates that most of the spin entropy (∼92%) has already been released above TN, which supports the picture of consecutive spin entropy reduction upon cooling with Te-bridged two-leg spin ladder system with strong intraladder and interladder couplings. Theoretical DFT+U calculations have been performed to search for the ground-state magnetic configuration and also to evaluate exchange-coupling constants that support the magnetic model deduced from the combined spin susceptibility and crystal structure symmetry analysis.