The magnetic properties of Sr2FeMoO6 oxides are investigated over a broad temperature range extending from 10 K to 800 K. It is found that the magnetization fully saturates at low temperatures at a value of 3.75 μB. In the paramagnetic regime, above the Curie temperature (TC≈420 K), the magnetic susceptibility can be well described by a Curie-Weiss law. It is found that the experimental effective moment μ*eff is gradually reduced under a field, an effect that can be attributed to some non-intrinsic behaviour. By means of detailed data analysis, it is shown that the paramagnetic effective moment μeff is close to that expected for a 3d6:4d0 atomic configuration. This result is interpreted as due to some electronic charge transfer from the itinerant 4d0(Mo) towards the 3d5(Fe) orbitals in the paramagnetic phase. We have also observed that the paramagnetic Curie temperature θP is positive and that θP≈TC, thus suggesting that the nearest-neighbour magnetic interactions are ferromagnetic in nature. These observations strongly support a double-exchange picture for the ferromagnetic coupling in these oxides.