Terephthalic acid, 2,5-furandicarboxylic acid and 1,8-octanediol were adopted as monomers and antimony trioxide as catalyst, and poly(terephthalic acid-2,5-furandicarboxylic acid-1,8-octanediol) copolyesters identified as PEOT-x, where x is the mole fraction of furandicarboxylic acid in the samples, were synthesized by direct esterification. The molecular structure of the copolyesters was characterized by FTIR and 1H NMR spectroscopy. Gel permeation chromatography (GPC), differential scanning calorimetry (DSC), and thermogravimetric analysis (TGA) were used to characterize the molecular weight, molar mass dispersity, glass transition temperature, and thermal stability of the copolyesters, respectively. The mechanical properties of the samples were also investigated. The number-average molecular weight (Mn) of the samples varies from 9 700–18 800 g/mol, and molar mass dispersity (Đ = Mw/Mn) from 2.15–3.34. The initial decomposition temperature of the copolyesters is in the 332–356 °C range, with maximum decomposition rates at 390–410 °C, while the glass transition temperature (Tg) varies from 0–33 °C. Mechanical test shows that PEOT-10 has the highest tensile strength, while PEOT-90 has the largest tensile modulus and elongation at break. The experimental results show that these copolyesters can be synthesized with relatively high molecular weights, good thermal stability, and fair mechanical properties, which makes them excellent replacements for commercial polyesters, such as PET, and these properties can be tuned through the relative amounts of biomass monomer 2,5-furandicarboxylic acid used in the reactions.