Novel biobased multiblock polyesters poly(2,5-furandimethylene succinate)-b-poly(butylene succinate) (PFS-PBS) containing PFS and PBS blocks were synthesized in a full composition range via chain-extension reaction of dihydroxyl terminated poly(2,5-furandimethylene succinate) (HO-PFS-OH) and poly(butylene succinate) (HO-PBS-OH) prepolymers. High molecular weight polyesters were obtained, and the stability of double bonds in 2,5-bis(hydroxymethyl)furan was guaranteed via this preparation procedure. The obtained copolyesters were characterized with H-1 NMR, gel permeation chromatography, differential scanning calorimetry, thermogravimetric analysis, polarized optical microscopy, wide-angle Xray diffraction, and the mechanical properties were also investigated. No transesterfication reaction happened during chain extension reaction, and the expected multiblock chemical structure was obtained. The PBS block is crystallizable, while the PFS block is nearly amorphous. Crystallization temperature and degree of crystallinity gradually decreased with increasing PFS fraction, but the melting temperature of crystalline samples showed no sharp reduction (109.4-105.2 degrees C). The crystallization rate also decreased with incorporation of PFS during isothermal crystallization, but the crystallization mechanism remained unchanged at any composition. Finally, the PFS-PBS copolyesters exhibit widely tunable mechanical properties, ranging from semicrystalline thermoplastics to amorphous soft elastomer-like polymers.