Direct measurements of a collisionless current channel during driven magnetic reconnection are obtained for the first time on the Versatile Toroidal Facility. The size of the diffusion region is found to scale with the electron drift orbit width, independent of the ion mass and plasma density. Based on experimental observations, analytic expressions governing the dynamical evolution of the current profile and the formation of the electrostatic potential that develops in response to the externally imposed reconnection drive are established. This time response is closely linked to the presence of ion polarization currents.