Electrospun cellulose acetate (eCA) and its hybrid with nanoaggregates of hydroxyapatite (eCA-nHA) were developed as potential and novel materials for bone tissue engineering purposes. Cultured human osteoblasts were seeded on eCA and eCA-nHA scaffolds, after which cell proliferative capacity and viability were studied using complementary assays. The interactions between the cells and the scaffolds were further characterized by scanning electron microscopy (SEM). These studies demonstrated that the scaffolds supported cell growth, as evidenced by continued cell proliferation for up to 3 days of exposure. Moreover, the osteoblasts remained viable and metabolically active while exposed to the scaffolds. SEM images detailed the tight interactions between the cell membranes and electrospun fibers. The presence of the hydroxyapatite nanoaggregates appeared to enhance osteoblast attachment, while allowing the cells to spread out along the fibers. These studies show that both eCA fiber and eCA-nHA fibrous nanoeomposite scaffolds hold promise for bone tissue engineering applications.