We report development of a highly accurate (parts per billion) absolute magnetometer based on ^{3}He NMR. Optical pumping polarizes the spins, long coherence times provide high sensitivity, and the ^{3}He electron shell effectively isolates the nuclear spin providing accuracy limited only by corrections including materials, sample shape, and magnetization. Our magnetometer was used to confirm calibration, to 32 ppb, of the magnetic-field sensors used in recent measurements of the muon magnetic moment anomaly (g_{μ}-2), which differs from the standard model by 2.4 ppm. With independent determination of the magnetic moment of ^{3}He, this work will lead the way to a new absolute magnetometry standard.