Using a first-principles Green function approach we study magnetic properties of the magnetic binary tetradymite chalcogenides Bi₂Se₃, Bi₂Te₃, and Sb₂Te₃. The magnetic coupling between transition-metal impurities is long range, extends beyond a quintuple layer, and decreases with increasing number of d electrons per 3d atom.We find two main mechanisms for the magnetic interaction in these materials: the indirect exchange interactionmediated by free carriers and the indirect interaction between magnetic moments via chalcogen atoms. The calculated Curie temperatures of these systems are in good agreement with available experimental data. Our results provide deep insight into exchange interactions in magnetic binary tetradymite chalcogenides and open a way to design new materials for promising applications.