According to previous theoretical work, the binary oxide CuO can become a room-temperature multiferroic via tuning of the superexchange interactions by application of pressure. Thus far, however, there has been no experimental evidence for the predicted room-temperature multiferroicity. Here, we show by neutron diffraction that the multiferroic phase in CuO reaches 295 K with the application of 18.5 GPa pressure. We also develop a spin Hamiltonian based on density functional theory and employing superexchange theory for the magnetic interactions, which can reproduce the experimental results. The present Letter provides a stimulus to develop room-temperature multiferroic materials by alternative methods based on existing low temperature compounds, such as epitaxial strain, for tunable multifunctional devices and memory applications.