Ordered arrays of semiconductor quantum dots may provide new electronic, optical, or thermoelectric functionalities. In this work, we create ordered two-dimensional arrays of Si-Ge quantum dots by heteroepitaxial growth on Si (001) with pre-patterned pits. Instead of growing the dots directly at elevated temperatures, we first grow conformal alloy layers and then use post-growth annealing to promote directed self-assembly. Annealing provides monodisperse size distributions with excellent control over the quantum dot (QD) mean size and shape. Similar to QD formation during growth, intermixing with substrate Si occurs, despite the conformal layer, due to the presence of the pattern topography itself.