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Room temperature x-ray diffraction, magnetization and neutron diffraction measurements up to 500 K have been carried out on polycrystalline bulk double perovskites AA'FeMoO6 (AA' = Ba2, BaSr, Sr2, Ca2) in order to determine and correlate their structural and magnetic properties. As the average ionic radius is diminished, the crystallographic structure evolves from cubic (for AA' = Ba2, BaSr) to tetragonal (Sr2) and finally to monoclinic (Ca2). In the case of AA' = Sr2, a novel crossover from a high temperature paramagnetic cubic state to a low temperature ferrimagnetic tetragonal state has been observed. For all the studied compounds, neutron diffraction patterns and magnetization measurements are consistent with a ferrimagnetic ordering of the Fe and Mo sublattices. A remarkable correlation is found between the Curie temperature and the electronic bandwidth, which is controlled by structural parameters.