The results of studying the photoluminescence of nanoheterostructures with multiple Ge1-x-ySixSny/Si quantum wells grown by molecular beam epitaxy on silicon substrates and annealed at different temperatures are presented. As a result of the annealing of the structures, a multifold increase in the intensity of the luminescence peak close in energy to the optical transitions within the multiple quantum wells is observed. The optimal annealing temperature and duration are determined in terms of the intensity of photoluminescence. The luminescent properties of a series of annealed Ge0.93-xSixSn0.07/Si structures with different Ge compositions are investigated. As a result, a shift of the low-temperature photoluminescence peak towards lower energies with an increase in the fraction of germanium in the alloy composition is shown. Thus, the possibility of controlling the luminescence spectrum of Ge0.93-xSixSn0.07/Si nanoheterostructures in the wavelength range of 1.3 −2.0 µm is demonstrated.