A two‐step synthesis of high‐molecular‐weight and bio‐based poly(butylene succinate) (PBS) from succinic anhydride and butane‐1,4‐diol is established, in which the first step is a 12 h atmospheric polycondensation at 95 °C in the presence of succinic acid. The subsequent polymerization, catalyzed by Novozym 435 suspended in toluene, yields PBS with a molecular weight above 73 000 g mol−1. The recovered lipase catalyst appears to give similar performance after six cycles. The versatility of this atmospheric synthetic route to PBS copolymers is validated through the syntheses of poly(butylene succinate‐co‐butylene malate) (PBSM), poly(butylene succinate‐co‐butylene fumarate) (PBSF), and poly(butylene succinate‐co‐butylene terephthalate) (PBST), in which succinic acid is replaced by corresponding di‐acids as monomers.