The structural characterization of fluorinated zigzag (4,0), (6,0), (8,0) and (10,0) single walled carbon nanotubes (F-SWCNT) has been investigated theoretically using C-13 and F-19 NMR spectroscopy. The functional groups NH, NCH3, NCH2OH, CH2NHCH2 and (CH2)(2)COOH have been attached covalently in (8,0) F-SWCNT and the corresponding changes in C-13 and F-19 chemical shift signatures have been examined. The binding energy, charge and bond length variation due to fluorination are reported. A set of isotropic and anisotropic chemical shift variables is deduced from the Gauge Includinlncluding Projector Augmented Wave (GIPAW) computations of the F-19 and C-13 nuclei in Pristine and F-SWCNTs. We show that the F-19 chemical shift parameters are better structural markers than their C-13 counterparts to clearly reveal the nanotube diameter dependency and the type of functional groups which are attached to the fluoronanotubes.