With nonperturbative laser-induced fluorescence measurements of ion flow, we confirm numerical simulations of spontaneous electric double-layer (DL) formation in a current-free expanding plasma. Measurements in two different experiments confirm that the DL is localized to the region of rapidly diverging magnetic field. The measurements indicate that the trapped ion population is a single Maxwellian, that the spatial gradient of the energy of ions accelerated through the DL matches the magnetic field gradient, and that DL formation is triggered when the ion-neutral collisional mean-free path exceeds the magnetic field gradient scale length.