  The leading quantum electrodynamic corrections to the nuclear magnetic
shielding in one- and two-electron atomic systems are obtained in a complete
form, and the shielding constants of $^1$H, $^3$He$^+$, and $^3$He are
calculated to be $17.735\,436(3) \cdot 10^{-6}$, $35.507\,434(9)\cdot 10^{-6}$,
and $59.967\,029(23)\cdot 10^{-6}$, respectively. These results are orders of
magnitude more accurate than previous ones, and, with the ongoing measurement
of the nuclear magnetic moment of $^3$He$^+$ and planned $^3$He$^{2+}$, they
open the window for high-precision absolute magnetometry using $^3$He NMR
probes. The presented theoretical approach is applicable to all other light
atomic and molecular systems, which facilitates the improved determination of
magnetic moments of any light nuclei.
