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