Recent advances in III1-xMnxV ferromagnetic semiconductors (for example in Ga1-xMnxAs) have demonstrated that electrical control of their spin properties can be used for manipulation and detection of magnetic signals(1,2). The Mn2+ ions in these alloys provide magnetic moments, and at the same time act as a source of valence-band holes that mediate the Mn2+-Mn2+ interactions(3-5). This coupling results in the ferromagnetic phase. In earlier work(2,6) it was shown that the ferromagnetic state can be enhanced or suppressed by varying the carrier density. Here we demonstrate that, by using hydrostatic pressure to continuously tune the wavefunction overlap, one can control the strength of ferromagnetic coupling without any change in the carrier concentration. Tuning the exchange coupling by this process increases the magnetization spectacularly, and can even induce the ferromagnetic phase in an initially paramagnetic alloy. These results may open new directions for strain-engineering of nanodevices.