Topological superconductors (TSCs), featuring fully gapped bulk and gapless surface states as well as Majorana fermions, have potential applications in fault-tolerant topological quantum computing. Because TSCs are very rare in nature, an alternative way to study the TSC is to artificially introduce superconductivity into the surface states of a topological insulator through the proximity effect [X. L. Qi, T. L. Hughse, S. Raghu, and S. C. Zhang, Phys. Rev. Lett. 102, 187001 (2009); L. Fu and C. L. Kane, Phys. Rev. Lett. 100, 096407 (2008); J. Alicea, Rep. Prog. Phys. 75, 076501 (2012); C. W. J. Beenakker, Annu. Rev. Condens. Matter Phys. 4, 113 (2013)]. Here we report the experimental realization of the proximity effect--induced TSC in ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$ thin films grown on a ${\mathrm{NbSe}}_{2}$ substrate, as demonstrated by the density of states probed using scanning tunneling spectroscopy. We observed Abrikosov vortices and Andreev lower energy bound states on the surface of the topological insulator, with the superconducting coherence length depending on the film thickness and the magnetic field. These results also indicate that the topological surface states of ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$ thin films are superconducting and, thus, that the ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}/{\mathrm{NbSe}}_{2}$ is an artificial TSC. The feasibility of fabricating a TSC with an individual Majorana fermion bound to a superconducting vortex for topological quantum computing is discussed.