We demonstrate by high resolution low temperature electron energy loss spectroscopy (EELS) measurements that the long range ferromagnetic (FM) order in vanadium (V)-doped topological insulator Sb$_2$Te$_3$ has the nature of van Vleck-type ferromagnetism. The positions and the relative amplitudes of two core-level peaks (L$_3$ and L$_2$) of the V EELS spectrum show unambiguous change when the sample is cooled from room temperature to T=10K. Magnetotransport and comparison of the measured and simulated EELS spectra confirm that these changes originate from onset of FM order. Crystal field analysis indicates that in V-doped Sb$_2$Te$_3$, partially filled core states contribute to the FM order. Since van Vleck magnetism is a result of summing over all states, this magnetization of core level verifies the van Vleck-type ferromagnetism in a direct manner. ; Comment: 5 pages, 5 figures