Poly(ethylene succinate) (PES) with weight-average molecular weight above 60,000 g mol-1 was efficiently obtained by enzymatic ring opening polymerization of cyclic oligo(ethylene succinate)s c(ES)n, which in turn were prepared by lipase-catalysed cyclocondensation in solution of dimethyl succinate and ethylene glycol. The methodology was demonstrated to be also applicable to the synthesis of high molecular weight PES-copolyesters containing butylene succinate, e-hydroxycaproate or L-lactate units with a random distribution.