Magnetic scaffolds for bone tissue engineering based on a poly(ε-caprolactone) (PCL) matrix and iron oxide (Fe3O4) magnetic nanoparticles were designed and developed through a three-dimensional (3D) fiber-deposition technique. PCL/Fe3O4 scaffolds were characterized by a 90/10 w/w composition. Tensile and magnetic measurements were carried out, and nondestructive 3D imaging was performed through microcomputed tomography (Micro-CT). Furthermore, confocal analysis was undertaken to investigate human mesenchymal stem cell adhesion and spreading on the PCL/Fe3O4 nanocomposite fibers. The results suggest that nanoparticles mechanically reinforced the PCL matrix; the elastic modulus and the maximum stress increased about 10 and 30%, respectively. However, the maximum strain decreased about 50%; this suggested an enhanced brittleness. Magnetic results evidenced a superparamagnetic behavior for these nanocomposite scaffolds. Micro-CT suggested an almost uniform distribution of nanoparticles. Confocal analysis highlighted interesting results in terms of cell adhesion and spreading. All of these results show that a magnetic feature could be incorporated into a polymeric matrix that could be processed to manufacture scaffolds for advanced bone tissue engineering and, thus, provide new opportunity in terms of scaffold fixation and functionalization.