We report the spark discharge synthesis of aerosol germanium nanoparticles followed by sintering in a tube furnace at different temperatures varying from 25 to 800 °C. The size, structure, chemical composition and optical properties were studied. We have demonstrated a melting mechanism of nanoparticles agglomerates, the growth of the mean primary particle size from 7 to 51 nm and the reduction of the size of agglomerates with a temperature increase. According to transmission electron microscopy (TEM) and Fourier transform infrared (FTIR) data, primary nanoparticles sintered at temperatures from 25 to 475 °C basically have a structure of Ge crystals embedded in a GeOx amorphous matrix, as well as visible photoluminescence (PL) with the maximum at 550 nm. Pure germanium nanoparticles are prepared at temperatures above 625 °C and distinguished by their absence of visible PL. The shape of the experimental UV-vis-NIR extinction spectra significantly depends on the size distribution of the germanium crystals. This fact was confirmed by simulations according to Mie theory for obtained ensembles of germanium nanoparticles.