Hierarchical structures, constituted by polymeric nano and microfibers, have been considered promising scaffolds for tissue engineering strategies, mainly because they mimic, in some way, the complexity and nanoscale detail observed in real organs. The chondrogenic potential of these scaffolds was already demonstrated, but their osteogenic potential is not corroborated yet. In order to assess if a hierarchical structure, with nanoscale details incorporated, is an improved scaffold for bone tissue regeneration, we evaluate cell adhesion, proliferation, and osteogenic differentiation of human Wharton’s jelly derived stem cells (hWJSCs), seeded into hierarchical fibrous scaffolds. Biological data corroborates that hierarchical fibrous scaffolds show an enhanced cell entrapment when compared to rapid prototyped scaffolds without nanofibers. Furthermore, upregulation of bone specific genes and calcium phosphate deposition confirms the successful osteogenic differentiation of hWJSCs on these scaffolds. These results support our hypothesis that a scaffold with hierarchical structure, in conjugation with hWJSCs, represents a possible feasible strategy for bone tissue engineering applications.