The decay of the ground-state two-proton emitter 45Fe was studied with a time-projection chamber and the emission of two protons was unambiguously identified. The total decay energy and the half-life measured in this work agree with the results from previous experiments. The present result constitutes the first direct observation of the individual protons in the two-proton decay of a long-lived ground-state emitter. In parallel, we identified for the first time directly two-proton emission from 43Cr, a known beta-delayed two-proton emitter. The technique developed in the present work opens the way to a detailed study of the mechanism of ground state as well as beta-delayed two-proton radioactivity.