The xenon and fluorine magnetic shielding tensors, sigma, of XeF2 are characterized using solid-state Xe-129 and F-19 NMR spectroscopy and nonrelativistic and spin-orbit relativistic zeroth-order regular approximation density functional theory (ZORA DFT). Analysis of Xe-129 and F-19 NMR spectra acquired with magic-angle spinning at several spinning rates indicates that the Xe and F magnetic shielding tensors are axially symmetric, as dictated by the crystal symmetry. The isotropic Xe-129 chemical shift is -1603 +/- 5 ppm with respect to OXeF4 (neat liquid, 24 degreesC) and the Xe magnetic shielding anisotropy, Omega, is 4245 +/- 20 ppm, the first anisotropy measured directly for a xenon compound. The parallel component of the experimentally determined xenon chemical shift tensor, delta(parallel to) = -4433 ppm differs from delta(Xe(free atom)) by similar to1000 ppm, providing the first experimental demonstration that relativistic effects play an important role in the nuclear magnetic shielding for xenon. Both the sign and magnitude of the isotropic indirect Xe-129,F-19 nuclear spin-spin coupling constant are determined, -5560 +/- 50 Hz. Analysis of the F-19 NMR spectra yield Omega(F) = 150 +/- 20 ppm. The ZORA DFT method has been employed to calculate sigma(Xe) and sigma(F) for isolated XeF2 and XeF4 molecules, as well as sigma(Kr) and sigma(F) for an isolated KrF2 molecule, at the relativistic and nonrelativistic levels of theory. Spin-orbit relativistic DFT results for Omega(Xe) are in very good agreement with those determined experimentally and highlight the importance of relativistic effects.