The chemical diversity and complexity of tellurium minerals were analyzed using the concept of mineral systems and Shannon informational entropy. The study employed data for 176 Te mineral species known today. Tellurium minerals belong to six mineral systems in the range of one-to-six species-defining elements. For 176 tellurium minerals, only 36 chemical elements act as essential species-defining constituents. The numbers of minerals of main elements are calculated as follows (the number of mineral species is given in parentheses): O (89), H (48), Cu (48), Pb (43), Bi (31), S (29), Ag (20), Fe (20), Pd (16), Cl (13), and Zn (11). In accordance with their chemistry, all Te minerals are classified into five types of mineral systems: tellurium, oxides, tellurides and intermetalides, tellurites, and tellurates. A statistical analysis showed positive relationships between the chemical, structural, and crystallochemical complexities and the number of essential species-defining elements in a mineral. A positive statistically significant relationship between chemical and structural complexities was established. It is shown that oxygen-free and oxygen-bearing Te minerals differ sharply from each other in terms of chemical and structural complexity, with the first group of minerals being simpler than the second group. The oxygen-free Te minerals (tellurium, tellurides, and intermetallides) are formed under reducing conditions with the participation of hydrothermal solutions. The most structurally complex oxygen-bearing Te minerals originate either from chemical weathering and the oxidation of ore deposits or from volcanic exhalations (Nabokoite).