It is demonstrated that ultrafast generation of ferromagnetic order can be achieved by driving a material from an antiferromagnetic to a ferromagnetic state using femtosecond optical pulses. Experimental proof is provided for chemically ordered FeRh thin films. A subpicosecond onset of induced ferromagnetism is followed by a slower increase over a period of about 30 ps when FeRh is excited above a threshold fluence. Both experiment and theory provide evidence that the underlying phase transformation is accompanied, but not driven, by a lattice expansion. The mechanism for the observed ultrafast magnetic transformation is identified to be the strong ferromagnetic exchange mediated via Rh moments induced by Fe spin fluctuations.