The crystal and magnetic structures of double perovskites of the type Ba2-xSrxYOsO6 were studied by synchrotron X-ray and neutron powder diffraction methods, bulk magnetic susceptibility measurements, and X-ray absorption spectroscopy. The structures were refined using combined neutron and synchrotron data sets based on an ordered array of corner-sharing YO6 and OsO6 octahedra, with the Ba/Sr cations being completely disordered. The structure evolves from cubic to monoclinic Fm3̅m (x ≈ 0.6) → I4/m (x ≈ 1.0) → I2/m (x ≈ 1.6) → P21/n as the Sr content is increased, due to the introduction of cooperative tilting of the octahedra. Bulk magnetic susceptibility measurements demonstrate the oxides are all anti-ferromagnets. The decrease in symmetry results in a nonlinear increase in the Neel temperature. Low-temperature neutron diffraction measurements of selected examples show these to be type-I anti-ferromagnets. X-ray absorption spectra collected at the Os L3- and L2-edges confirm the Os is pentavalent in all cases, and there is no detectable change in the covalency of the Os cation as the A-cation changes. Analysis of the L3/L2 branching ratio shows that the spin-orbit coupling is constant and insignificant across the series.