Borosilicate bioactive glasses (BBGs) have shown the capacity to promote higher formation of new bone when compared with silicate bioactive glasses. Herein, we assessed the capacity of BBGs to induce osteogenic differentiation of bone marrow mesenchymal stem cells (BM-MSCs) as a function of their substituted divalent cations (Mg, Ca, Sr). To this purpose, we synthesized BBG particles by melt quenching. The cell viability, proliferation, and morphology (i.e., PrestoBlue, PicoGreen, and DAPI and Phalloidin stainings, respectively), as well as protein expression (i.e., alkaline phosphatase, ALP; osteopontin, OP; and osteocalcin, OC), of BM-MSCs in contact with BBGs were evaluated for 21 days. We observed an enhanced expression of bone-specific proteins (ALP, OP, and OC) and high mineralization of BM-MSCs under BBG-Mg and BBG-Sr-conditioned osteogenic media for concentrations of 20 and 50 mg/mL with low cytotoxic effects. Moreover, BBG-Sr, at a concentration of 50 mg/mL, was able to increase the mineralization and expression of the same bone-specific proteins even under basal medium conditions. These results indicated that the proposed BBGs improved osteogenic differentiation of BM-MSCs, therefore showing their potential as relevant biomaterials for bone tissue regeneration, not only by bonding to bone tissue but also by stimulating new bone formation.