Boron neutron capture therapy (BNCT) has been recognized as a very promising approach for cancer treatment. In the case of osteosarcoma, boron-containing scaffolds can be a powerful tool to combine boron delivery to the tumor cells and the repair of postoperative bone defects. Here we describe the fabrication and characterization of novel biodegradable polymer composites as films and 3D-printed matrices based on aliphatic polyesters containing closo-borates (CB) for BNCT. Different approaches to the fabrication of composites have been applied, and the mechanical properties of these composites, kinetics of their degradation, and the release of closo-borate have been studied. The most complex scaffold was a 3D-printed poly(ε-caprolactone) matrix filled with CB-containing alginate/gelatin hydrogel to enhance biocompatibility. The results obtained allowed us to confirm the high potential of the developed composite materials for application in BNCT and bone tissue regeneration.