In this work, a poly(L-lactide-co-glycolide) (PLGA)-based composite was enriched with one of the following sol-gel bioactive glasses (SBG) at 50 wt.%: A1—40 mol% SiO2, 60 mol% CaO, CaO/SiO2 ratio of 1.50; S1—80 mol% SiO2, 20 mol% CaO, CaO/SiO2 ratio of 0.25; A2—40 mol% SiO2, 54 mol% CaO, 6 mol% P2O5, CaO/SiO2 ratio of 1.35; S2—80 mol% SiO2,16 mol% CaO, 4 mol% P2O5, CaO/SiO2 ratio of 0.20. The composites and PLGA control sheets were then soaked for 24 h in culture media, and the obtained condition media (CM) were used to treat human bone marrow stromal cells (hBMSCs) for 72 h. All CMs from the composites increased ERK 1/2 activity vs. the control PLGA CM. However, expressions of cell migration-related c-Fos, osteopontin, matrix metalloproteinase-2, C-X-C chemokine receptor type 4, vascular endothelial growth factor, and bone morphogenetic protein 2 were significantly increased only in cells treated with the CM from the A1/PLGA composite. This CM also significantly increased the rate of human BMSC migration but did not affect cell metabolic activity. These results indicate important biological markers that are upregulated by products released from the bioactive composites of a specific chemical composition, which may eventually prompt osteoprogenitor cells to colonize the bioactive material and accelerate the process of tissue regeneration.