In this Letter we report the first experimental observation of the double emittance minimum effect in the beam dynamics of high-brightness electron beam generation by photoinjectors; this effect, as predicted by the theory, is crucial in achieving minimum emittance in photoinjectors aiming at producing electron beams for short wavelength single-pass free electron lasers. The experiment described in this Letter was performed at the SPARC photoinjector site, during the first stage of commissioning of the SPARC project. The experiment was made possible by a newly conceived device, called an emittance meter, which allows a detailed and unprecedented study of the emittance compensation process as the beam propagates along the beam pipe.