The structure of (GeTe4)(1-x)(AgI)(x) (x=0.15 and 0.25) glasses has been investigated by X-ray and neutron diffraction as well as extended X-ray absorption spectroscopy (EXAFS) and Raman spectroscopy. Large-scale structural models have been obtained by fitting simultaneously the experimental datasets in the framework of the reverse Monte Carlo simulation technique (RMC). Short-range order parameters have been calculated and compared with that of GeTe4. Doping with AgI affects the structure of the host GeTe4 matrix in two ways. First, while Te is essentially twofold coordinated in GeTe4, its coordination number is as high as similar to 2.9 +/- 0.3 for x=0.25. The change is mainly due to the increased fraction of Te-Te bonds. Second, Ge atoms remain fourfold coordinated but the tetrahedral symmetry is distorted due to the elongation of some Ge-Te bonds. The incorporation of AgI in the GeTe4-based host covalent matrix and the Te coordination increase explains the enhanced thermal stability of (GeTe4)(1-x)(AgI)(x) in the supercooled liquid-state hindering the crystallization of Te found in case of GeTe4 glass.