For Ge nanodots approximately 20 nm in diameter grown by annealing a thin amorphous Ge layer deposited by molecular beam epitaxy on a mesoporous TiO2 layer on Si(001), photoluminescence (PL) was observed as a wide near-infrared band near 800 meV. Using a tight binding theoretical model, the energy-dependent PL spectrum was transformed into a dependence on dot size. The average dot size determined the peak energy of the PL band and its shape depended on the size distribution, including bandgap enlargement due to quantum confinement. Combining the dot sample PL with an established dependence of emission efficiency on dot diameter, it was possible to derive a dot size distribution and compare it with results obtained independently from atomic force microscopy.