The search for ferromagnetism above room temperature in dilute magnetic semiconductors has been intense in recent years. We report the first observations of ferromagnetism above room temperature for dilute (<4 at.%) Mn-doped ZnO. The Mn is found to carry an average magnetic moment of 0.16 mu(B) per ion. Our ab initio calculations find a valance state of Mn(2+) and that the magnetic moments are ordered ferromagnetically, consistent with the experimental findings. We have obtained room-temperature ferromagnetic ordering in bulk pellets, in transparent films 2-3 microm thick, and in the powder form of the same material. The unique feature of our sample preparation was the low-temperature processing. When standard high-temperature (T > 700 degrees C) methods were used, samples were found to exhibit clustering and were not ferromagnetic at room temperature. This capability to fabricate ferromagnetic Mn-doped ZnO semiconductors promises new spintronic devices as well as magneto-optic components.