Density functional theory (DFT) is employed based on the generalized gradient approximation (GGA), including the Hubbard (U) parameter, to investigate the modification of the electronic properties of GaN nanowires (NWs) by Eu dopants introduced via Eu-associated defect complexes to explore the origin of magnetic characteristics. These findings show that incorporating Eu dopants, including Eu-intrinsic defect complexes, in GaN NWs leads to a significant change in the electronic properties of GaN, as evident from p-f state hybridization, resulting in unique magnetic characteristics. However, while Ga-vacancies (VGa) in Eu-doped GaN NWs impart a significant magnetic moment on N atoms, N-vacancies (VN) produce a negligible effect on the magnetic properties of NWs. To predict the magnetic exchange effect, two Eu3+ ions are introduced in the NWs, showing that the complex with two Eu atoms and Ga-vacancy (2Eu-VGa) induces stable ferromagnetism above room temperature.