Polybutylene succinate (PBS) nanocomposite materials were prepared using a melt compounding process. The Mg2Al-based PBS nanocomposites, dispersed with inorganic–organic hybrid materials (layered double hydroxides, LDHs), were functionalized with the amino acids L-histidine (HIS) and L-phenylalanine (PHE). The rheological and anti-ultraviolet (anti-UV) properties were investigated and compared to filler-free PBS as well as LDH Mg2Al/nitrate as references. Both organo-modified LDHs exhibited a remarkable chain-extension effect for PBS with an outstanding increase in the zero-shear viscosity η0 for PBS–Mg2Al/PHE (two order of magnitude increase as compared to filler-free PBS). These results were compared to data found in the literature. Moreover, HIS and PHE anions embedded into the LDH structure can successfully prevent the chain scission reactions that usually occur during photo-ageing of PBS under UV radiation exposure. This highlights the outstanding performance of the LDH hybrid materials, and in particular, their application as a polymer chain extender and UV stabilizer for PBS, which can likely be extended to other biodegradable polymers.