We successfully obtained Sn-doped SrTiO${}_{3}$ (SSTO) perovskites, and clarified their ferroelectricity and structural properties by using first-principles theoretical calculations. The ferroelectricity of SSTO was confirmed by the appearance of a dielectric permittivity maximum and a clear hysteresis loop of the relationship between the external electric field and the electric flux density below 180 K. X-ray diffraction and Raman spectra revealed the structural phase transition of SSTO at approximately 200 K. We directly observed by spherical aberration corrected scanning transmission electron microscopy with energy-dispersive x-ray spectroscopy that Sn ions are doped into both Sr and Ti sites (Sn${}_{A}$ and Sn${}_{B}$), and that Sn${}_{A}$ is located at an off-centered position. We also performed theoretical analyses of SSTO and related perovskites, and found that Sn${}_{A}$ is preferentially located in an off-centered position and that Sn${}_{A}$ and the O${}_{6}$ octahedron, which includes Sn${}_{B}$ in its center, oscillate along the antiphase direction in the soft mode. Thus, we propose that the ferroelectricity of SSTO originates from the antiphase off-centering, which induces ferroelectric nanoregions in paraelectric SrTiO${}_{3}$.