Sustainable, biodegradable and thermoplastic processable aliphatic polyesters (polybutylene succinate (PBS) and polyethylene succinate (PES)) were prepared and characterized; then, they were grafted onto cellulose micro-fibers using a simple click reaction. This modification was conducted under simple experimental conditions. The characterization (NMR and FTIR analysis), thermal properties, solubility, morphology and biodegradation process of the all products prepared were established and studied. The results show that the solubility of the prepared derivatives is improved in comparison with cellulose, while their thermal stability showed a slight decrease compared to the starting materials. The composites derived from the modified cellulose show a slight decrease in their biodegradability in comparison with that of unmodified cellulose due to several parameters.