We present here an ab initio study of the structural, magnetic, and hyperfine properties of Fe-doped rutile SnO₂ for different concentrations and distributions of the Fe atoms and oxygen vacancies in the SnO₂ host. The calculated results are compared with experimental ones obtained by Mössbauer spectroscopy and X-ray absorption techniques. This comparison enables us to characterize the local structure around Fe atoms and to identify the different hyperfine interactions that are observed in samples prepared by different methods. It is concluded that oxygen vacancies are fundamental for the ferromagnetic response of Fe-doped SnO₂. The ab initio calculations show that two Fe ions sharing an oxygen vacancy are coupled ferromagnetically, forming a bound magnetic polaron (BMP), and that two neighbor BMPs are aligned antiparallel to each other. Electron doping plays a fundamental role mediating the magnetic coupling between the BMP inducing ferromagnetic alignment between the BMPs.