Precision measurements by the Alpha Magnetic Spectrometer (AMS) on the International Space Station of ^{3}He and ^{4}He fluxes are presented. The measurements are based on 100 million ^{4}He nuclei in the rigidity range from 2.1 to 21 GV and 18 million ^{3}He from 1.9 to 15 GV collected from May 2011 to November 2017. We observed that the ^{3}He and ^{4}He fluxes exhibit nearly identical variations with time. The relative magnitude of the variations decreases with increasing rigidity. The rigidity dependence of the ^{3}He/^{4}He flux ratio is measured for the first time. Below 4 GV, the ^{3}He/^{4}He flux ratio was found to have a significant long-term time dependence. Above 4 GV, the ^{3}He/^{4}He flux ratio was found to be time independent, and its rigidity dependence is well described by a single power law ∝R^{Δ} with Δ=-0.294±0.004. Unexpectedly, this value is in agreement with the B/O and B/C spectral indices at high energies.