Nanoscale fibers mimicking the extracellular matrix of natural tissue can be produced by conventional electrospinning, but this approach results in two-dimensional thin dense fibrous mats which can hinder effective cell infiltration. The aim of the present study was to design a thick, three-dimensional (3D) cylindrical scaffold with an open pore structure assembled from short polycaprolactone (PCL) fibers using a facile airbrushing approach. In addition, magnesium particles were incorporated into the PCL solution to both enhance the mechanical properties of the scaffold and stimulate cellular activity following cell seeding. Separated short composite airbrushed fibers were assembled into a 3D cylindrical structure by cold-press molding and thermal cross-linking. The microstructure, chemical composition, porosity and thermal properties were subsequently investigated, along with changes in mechanical performance following immersion in PBS for 60 d. The results showed that the assembled 3D fibrous 10 mm thick cylindrical matrix had an interconnected fibrous network structure with 31.5%–60% porosity. Encapsulation of the Mg particles into the 3D assembled fibrous scaffold enhanced the mechanical properties of the plain PCL scaffolds. The results also demonstrated controlled release of Mg ions into the PBS media for up to 60 d, as evaluated by changes in Mg ion concentration and pH of the media. In addition, the 3D fibrous assembled matrix was shown to support human osteoblast-like cell adhesion, proliferation and penetration. The results suggest that this novel fabrication method of biodegradable thick 3D scaffolds with an open pore structure is promising for the production of a new generation of 3D scaffolds for tissue regeneration applications.