The South Pole Telescope (SPT) has systematically identified 81 high-redshift, strongly gravitationally lensed, dusty star-forming galaxies (DSFGs) in a 2500 square degree cosmological millimeter-wave survey. We present the final spectroscopic redshift survey of this flux-limited (S
870 μm > 25 mJy) sample, initially selected at 1.4 mm. The redshift survey was conducted with the Atacama Large Millimeter/submillimeter Array across the 3 mm spectral window, targeting carbon monoxide line emission. By combining these measurements with ancillary data, the SPT sample is now spectroscopically complete, with redshifts spanning 1.9 5, making this the largest sample of high-redshift DSFGs to date, and enabling the “high-redshift tail” of extremely luminous DSFGs to be measured. Though galaxy formation models struggle to account for the SPT redshift distribution, the larger sample statistics from this complete and well-defined survey will help inform future theoretical efforts.