Fossil-based and true bio-based poly(butylene succinate) (PBS) prepolymers were synthesized and submitted to solid-state polymerization (SSP) in the proximity of the polyester melting point (Tm), for reaction times up to 29 h under flowing nitrogen. SSP acted as a postcrystallization process, imparting an increase of the PBS melting point up to 126 °C from a starting Tm of 112–114 °C. Adding a precrystallization step prior SSP even resulted in a 2.5 times increase of the initial MW and a Tm shift up to 128 °C. Furthermore, the effect of most critical process parameters on the SSP feasibility and effectiveness was assessed, so as to launch an appropriate operation profile. End-group imbalance turned out to be the most significant key parameter for PBS polymerizability, and various attempts were made toward correcting it. Finally, SSP was examined as a PBS recycling technique and efficiently “revived” hydrolyzed PBS structures.