The use of high-pressure synthesis conditions to produce I-bearing aluminoborosilicate represent a promising issue for the immobilization of 129I radioisotope. Furthermore, iodine appears to be more solubilized in glasses under its iodate (I5+) form rather than its iodide (I-) form. Currently, the local atomic environment for iodine is poorly constrained for I- and virtually unknown for I5+ or I7+. We used I K-edge X-ray Absorption Spectroscopy conducted at 20 K for determining the local atomic environment of iodine dissolved as I-, I5+, I7+ in a series of aluminoborosilicate glasses. We determined that I- is surrounded by either Na+ or Ca2+ in agreement with previous works. The signal collected from EXAFS reveals that I5+ is surrounded invariably by three oxygen atoms forming a IO3- cluster charge compensated by Na+ and/or Ca2+. The I-O distance in iodate dissolved in glass is comparable to the I-O distance in crystalline compounds at ~1.8 Å. The distance to the second nearest neighbor (Na+ or Ca2+) is also constant at ~3.2 Å. This derived distance is identical to the distance between I- and Na+ or Ca2+ in the case of iodide local environment. For one sample containing iodate and periodate, the distinction between the local environment of I5+ and I7+ could not be made suggesting that both environments have comparable EXAFS signal.