Influence of the Ge layer thickness and annealing conditions on the parameters of relaxed Ge/Si(001) layers grown by molecular beam epitaxy via two-stage growth is investigated. The dependences of the threading dislocation density and surface roughness on the Ge layer thickness, annealing temperature and time, and the presence of a hydrogen atmosphere are obtained. As a result of optimization of the growth and annealing conditions, relaxed Ge/Si(001) layers which are thinner than 1 μm with a low threading dislocation density on the order of 107 cm–2 and a root mean square roughness of less than 1 nm are obtained.