We present single-crystal growth and magnetic property studies of tellurium-bridged copper spin-1/2 system Ba$_2$CuTeO$_6$. 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 $chi$(T) data indicates that the triclinic Ba$_2$CuTeO$_6$ undergoes a stepwise crossover for exchange couplings revealed by a broad maximum near T$_{max}$$sim$75~K and an anisotropic cusp in $frac{dchi}{dT}$(T) to signify a three dimensional (3D) antiferromagnetic long-range ordering (LRO). The 3D LRO has been suggested from the anisotropic behavior of $chi$(T) with strong c-axis spin anisotropy and the signature of spin flop transition from the isothermal magnetization below $T_N$. Analysis of magnetic heat capacity (Cm) at $T_N$~15 K indicates that most of the spin entropy (~92% ) has already been released above $T_N$, 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.
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