Effects of postgrowth high-temperature annealing on vacancy complexes and photoluminescence (PL) from GeSiSn/Si multiple quantum wells (MQWs) are studied. The series of PL peaks related to the vacancy-tin complexes was observed for as-grown samples including different structures, such as GeSiSn/Si MQWs, multilayer periodic structure with GeSiSn quantum dots (QDs), GeSn cross-structures upon GeSiSn/Si MQWs, and thick GeSiSn layers. The PL band intensity is significantly reduced after annealing at 700 °C corresponding to the reduction in vacancy density, as demonstrated by the positron annihilation spectroscopy (PAS) data. Such annealing also results in the appearance of the PL signal related to the interband optical transitions in GeSiSn/Si MQWs. However, the high temperature could negatively impact the sharpness of heterointerfaces due to Sn diffusion, thus limiting the PL efficiency. To improve the luminescence properties of GeSiSn/Si structures, we proposed a two-stage technique combining both the annealing and subsequent treatment of samples in a hydrogen plasma at 200 °C. The plasma treatment significantly reduces the PL band of vacancy-related defects, whereas annealing at a moderate temperature of ∼600 °C prevents the blurring of heterointerfaces. As a result, we demonstrate an increase in the relative efficiency of interband PL of type II GeSiSn/Si MQW structures emitting in the range of 1.5–2 μm.