This paper describes the one-pot synthesis of a polyglycidol (PG)-based polymer, poly(ethoxyethyl glycidyl ether) (PEEGE)-b-[hyperbranched polyglycerol (hbPG)-co-PEEGE]x/y, its micelle formulation, and the ability to encapsulate a model therapeutic molecule. Amphiphilic block copolymers were prepared by the sequential addition of ethoxyethyl glycidyl ether (EEGE) to glycidol. The composition of the block copolymers varied from 62:38 to 92:8. Block copolymers with composition x:y≥66:34 were soluble only in organic solvents. Micelles were formulated by injection of deionized water into a tetrahydrofuran block copolymer solution with or without pyrene as a model hydrophobic molecule. The critical micelle concentration was 18.2-30.9 mg/L, and the micelle size was 100-250 nm. The pyrene-containing micelle rapidly collapsed on acidic exposure, allowing conversion of hydrophobic PEEGE to hydrophilic PG, thus, facilitating the release of the encapsulated pyrene. Cytotoxicity data showed high biocompatibility of PG-based block copolymers, suggesting their potential as a drug delivery carrier.