The van Cittert-Zernike theorem is extended to the vectorial regime based on spatial averaging over the observation plane, and experimental demonstrations are presented. The theorem connects complex vectorial source structure to the degree of coherence and polarization of the spatially fluctuating vectorial field in the far field. Experimentation is carried out by making use of the space averages as a replacement of ensemble averages for the Gaussian stochastic field. For quantitative comparison with the theorem, analytical and experimental results are presented for a rectangular aperture with different vectorial source structures.