We have studied the magnetic properties of (GaMnAs)(m)(GaAs)(n) superlattices with magnetic GaMnAs layers of thickness between eight and 16 molecular layers (ML) (23-45 Angstrom), and with non-magnetic GaAs spacers from 4 to 10 ML (11-28 Angstrom). While previous reports state that GaMnAs layers thinner than 50 Angstrom 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 non-magnetic GaAs spacer. The neutron scattering experiments have shown that the magnetic layers in superlattices are ferromagnetically coupled for both thin (below 50 Angstrom) and thick (above 50 Angstrom) GaMnAs layers.