A series of novel aliphatic polyesters with azido functional groups were synthesized via the direct lipase-catalyzed polycondensation of dialkyl diester, diol and 2-azido-1,3-propanediol (azido glycerol) using immobilized lipase B from Candida antarctica (CALB). The effects of polymerization conditions including reaction time, temperature, enzyme amount, substrates and monomer feed ratio on the molecular weights of the products were studied. The polyesters with pendant azido groups were characterized by ¹H NMR, ¹³C NMR, 2D NMR, FTIR, GPC and DSC. Alkyne end-functionalized poly(ethylene glycol) containing a cleavable acetal group was then grafted onto the polyester backbone by copper-catalyzed azide–alkyne cycloaddition (CuAAC, click chemistry). Using fluorescence spectroscopy, dynamic light scattering (DLS) and transmission electron microscopy (TEM), these amphiphilic graft copolymers were found to readily self-assemble into nanosized micelles in aqueous solution with critical micelle concentrations between 0.70 and 1.97 mg L⁻¹, and micelle sizes from 20–70 nm. The degradation of these polymers under acidic conditions was investigated by GPC and ¹H NMR spectroscopy. Cell cytotoxicity tests indicated that the micelles had no apparent cytotoxicity to Bel-7402 cells, suggesting their potential as carriers for controlled drug delivery.