The atomic structure of ultrathin iron films deposited on the (0001) surface of the topological insulator Bi₂Se₃ is analyzed by surface x-ray absorption spectroscopy. Iron atoms deposited on a Bi₂Se₃ (0001) surface kept at 160 K substitute bismuth atoms within the first quintuple layer. Iron atoms are neighbored by six selenium atoms at a distance in the 2.4 Å range indicating substantial atomic relaxations. Mild annealing up to 520 K leads to the formation of α-FeSe, characterized by a local order extending up to the sixth shell (5.80 Å). Ab initio calculations predict a noncollinear magnetic ordering with a transition temperature of 3.5-10 K depending on the iron concentration and the number of the layers in which Fe is located.