Precision measurements by the Alpha Magnetic Spectrometer (AMS) on the International Space Station of 3He and 4He fluxes are presented. The measurements are based on 100 million 4He nuclei in the rigidity range from 2.1 to 21 GV and 18 million 3He from 1.9 to 15 GV collected from May 2011 to November 2017. We observed that the 3He and 4He fluxes exhibit nearly identical variations with time. The relative magnitude of the variations decreases with increasing rigidity. The rigidity dependence of the 3He/4He flux ratio is measured for the first time. Below 4 GV, the 3He/4He flux ratio was found to have a significant long-term time dependence. Above 4 GV, the 3He/4He flux ratio was found to be time independent, and its rigidity dependence is well described by a single power law proportional to 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.