Bone tissue is one of the most transplanted tissues. The ageing population and bone diseases are the main causes of the growing need for novel treatments offered by bone tissue engineering. Three-dimensional (3D) scaffolds, as artificial structures that fulfil certain characteristics, can be used as a temporary matrix for bone regeneration. In this study, we aimed to fabricate 3D porous polymer scaffolds functionalized with tricalcium phosphate (TCP) particles for applications in bone tissue regeneration. Different combinations of poly(lactic acid) (PLA), poly(ethylene glycol) (PEG with molecular weight of 600 or 2000 Da) and poly(ε-caprolactone) (PCL) with TCP were blended by a gel-casting method combined with rapid heating. Porous composite scaffolds with pore sizes from 100 to 1500 µm were obtained. ATR-FTIR, DSC, and wettability tests were performed to study scaffold composition, thermal properties, and hydrophilicity, respectively. The samples were observed with the use of optical and scanning electron microscopes. The addition of PCL to PLA increased the hydrophobicity of the composite scaffolds and reduced their susceptibility to degradation, whereas the addition of PEG increased the hydrophilicity and degradation rates but concomitantly resulted in enhanced creation of rounded mineral deposits. The scaffolds were not cytotoxic according to an indirect test in L929 fibroblasts, and they supported adhesion and growth of MG-63 cells when cultured in direct contact.