A three-dimensional array of phototubes in deep ice at the South Pole called the Antarctic Muon and Neutrino Detector Array (AMANDA) is recording Cherenkov light pulses that serve as tracers of high-energy neutrinos from throughout the Universe. The performance of this neutrino observatory will ultimately be constrained by the optical properties of the ice at near-ultraviolet and visible wavelengths. At depths greater than ~1.4 km, air bubbles are absent and light travels great distances, limited only by absorption and scattering by dust in the ice. In this paper, the Mie theory is used to predict the magnitude and wavelength dependence of the scattering and absorption coefficients and mean cosine of the scattering angle for deep South Pole ice. The results depend on the composition, size distribution, and depth profile of insoluble mineral grains, sea salt grains, liquid acid droplets, and soot particles. With most probable values for mineral grains, sea salt, acid, and soot, we fit optical data in the wavelength interval of 300--500 nm for depths of 1.6--1.83 km, taken with pulsed laser beams as light sources and with AMANDA phototubes as receivers. Our work provides quantitative evidence that aerosols deposited in snow and compacted into the ice account for the optical properties at wavelengths ~300--500 nm. We finally predict optical properties of the South Pole ice at 2.5 km, a depth future AMANDA strings may reach. We expect that at 2.5 km the effective scattering, which is predominantly due to acid droplets, decreases by a factor of ~1.5 relative to that at 1.7 km and that absorption, which is predominantly due to the mineral and soot, decreases by a factor of ~3--5 relative to that at 1.7 km. ¿ 1998 American Geophysical Union