We report the results of a neutron diffraction study, carried out on both single crystalline and polycrystalline samples of Tb₅Si_2.2Ge_1.8 and polycrystalline Tb₅Si_2.5Ge_1.5. On cooling, at approximately 120 K, the Tb₅Si_2.2Ge_1.8 system undergoes a magnetoelastic transition from a high-temperature monoclinic-paramagnetic to a low-temperature orthorhombic-ferromagnetic structure. Between 120 K and 75 K, the magnetic structure has a net ferromagnetic component along the a axis direction. The moments are slightly canted with respect to the a axis, while the components along the b and c axes are ordered antiferromagnetically. A second magnetic transition occurs at approximately 75 K. Below this temperature, the magnetic structure consists of ferromagnetically aligned μ_x and μ_z projections of the magnetic moments and an antiferromagnetic arrangement of theμ_y moment components. Magnetic structures of Tb₅Si_2.5Ge_1.5 are nearly identical to those of Tb₅Si_2.2Ge_1.8.