Thermal treatment is a post-synthesis treatment that aims to improve the crystallinity and interrelated physical properties of as-prepared materials. This process may also cause some unwanted changes in materials like their oxidation or contamination. In this work, we present the post-synthesis annealing treatments of the amorphous Fe1−xCox (x = 0.25; 0.50; 0.75) Wire-like nanochains performed at 400 °C in two different atmospheres, i.e., a mixture of 80% nitrogen and 20% hydrogen and argon. These processes caused significantly different changes of structural and magnetic properties of the initially-formed Fe-Co nanostructures. All of them crystallized and their cores were composed of body-centered cubic Fe-Co phase, whereas their oxide shells comprised of a mixture of CoFe2O4 and Fe3O4 phases. However, the annealing carried out in hydrogen-containing atmosphere caused a decomposition of the initial oxide shell layer, whereas a similar process in argon led to its slight thickening. Moreover, it was found that the cores of thermally-treated Fe0.25Co0.75 nanochains contained the hexagonal closest packed (hcp) Co phase and were covered by the nanosheet-like shell layer in the case of annealing performed in argon. Considering the evolution of magnetic properties induced by structural changes, it was observed that the coercivities of annealed Fe-Co nanochains increased in comparison with their non-annealed counterparts. The saturation magnetization (MS) of the Fe0.25Co0.75 nanomaterial annealed in both atmospheres was higher than that for the non-annealed sample. In turn, the MS of the Fe0.75Co0.25 and Fe0.50Co0.50 nanochains annealed in argon were lower than those recorded for non-annealed samples due to their partial oxidation during thermal processing.