By using scanning tunneling microscopy we found that the surface reconstruction of Ge/Si(001) epilayers evolves from (M x N) to (2 x N), and eventually to (2 x 1), during exposure to a Si flux. This sequence appears to be just the inverse of that observed during the growth of Ge or SiGe alloys on Si(001). However, molecular dynamics simulations supported by ab initio calculations allow us to interpret this morphological evolution in terms of Si migration through the epilayer and complex Si-Ge intermixing below the top Ge layer.