We have studied the magnetic properties of (GaMnAs)m/(GaAs)n superlattices with magnetic GaMnAs layers of thickness between 8 and 16 molecular layers (ML) (23-45 AA), and with nonmagnetic GaAs spacers from 4 ML to 10 ML (11-28 AA). While previous reports state that GaMnAs layers thinner than 50 AA are paramagnetic in the whole Mn composition range achievable using MBE growth (up to 8% Mn), we have found that short period superlattices exhibit a paramagnetic-to-ferromagnetic phase transition with a transition temperature which depends on both the thickness of the magnetic GaMnAs layer and the nonmagnetic GaAs spacer. The neutron scattering experiments have shown that the magnetic layers in superlattices are ferromagnetically coupled for both thin (below 50 AA) and thick (above 50 AA) GaMnAs layers.