Self-assembled Ge nanodots were formed by in-situ thermal annealing of a thin amorphous Ge layer deposited by molecular beam epitaxy on a thin SiO₂ or TiO₂ layer on Si(001). The dot photoluminescence (PL) appeared primarily as a wide near-infrared band peaked near 800 meV. Using both the k•p and tight binding theoretical models, we have analyzed the PL spectrum in terms of the dot size distribution required to reproduce the observed asymmetric band shape. The peak energy of the PL band reflects the average dot size and its shape depends on the dot size distribution. The observed size distribution determined from transmission electron and atomic force microscopy allowed the determination of the nonlinear increase in the PL quantum efficiency with decreasing dot diameter. In addition, we show it is possible to evaluate the size distribution of Ge dots from their PL energy dependence.