The addition of small amounts of iodine to thermodynamically instable TeCl2 yields amorphous, glassy tellurium(II) halides TeCl2-xIx (0.1 < x < 0.5), which were prepared by rapid quenching of melts with the respective compositions. At ambient temperature, these glassy solids are sufficiently stable to be handled and investigated by analytical methods. High-energy X-ray diffraction and reverse Monte Carlo simulations of two compositions TeCl2-xIx, x = 0.1 and 0.5, show that these glasses are made up of structural fragments that are present in both tellurium tetrahalides and in low-valent tellurium subhalides. In both glasses, the Te-Te bonding shows narrow coordination distribution with a mean total coordination number for the Te atoms of 4.1 +/- 1.3 and a mean Te-Te coordination number of 0.7 +/- 0.7. Accordingly, the mean Cl-Te coordination number is 1.7 +/- 0.8 and the mean I-Te coordination number is 1.6 +/- 0.7. The medium-range order increases with increasing iodine content.