Stimuli-responsive block copolymer assemblies are a significant class of smart materials extensively studied for advanced applications such as drug- and gen-delivery systems. Different types of light- and temperature-responsive polymer assemblies containing photochromic spiropyran chain end groups, temperature-responsive poly (N-isopropylacrylamide) (PNIPAM) block, and hydrophobic poly (methyl methacrylate) (PMMA) block were developed. These amphiphilic block copolymers with the ability of self-assembly to micellar structures were synthesized using spiropyran-initiated atom transfer radical polymerization. Regarding the hydrophilic fraction (0.5<fphilic), the amphiphilic block copolymers were self-assembled to spherical micelles in aqueous media as confirmed by TEM images. The size of these polymer assemblies was changed in response to temperature changes and also UV light (365 nm) irradiation. The results of UV–Vis spectroscopy display that photochromic behavior, the kinetics of spiropyran (SP) to merocyanine (MC) and MC to SP isomerizations were significantly affected by the polarity of the polymer blocks in neighboring of the spiropyran chain end group. The lower critical solution temperature (LCST) of PNIPAM shows a shift from 26.5 to 37.5 °C after isomerization of the SP to MC, as a result of increase of its polarity and water-solubility. The doxorubicin (DOX) release can be controlled by pH, temperature, and light by using of multi-responsive block copolymer micelles as smart drug carriers. The release efficiency was reached to 60–85% at pH 5.3, 80–90% at temperatures of above LCST of PNIPAM (40 °C), and also 90–100% under UV irradiation after 48 h. The results display that stimuli-responsive polymer assemblies based on amphiphilic block copolymers containing spiropyran chain end groups are applicable in smart drug-delivery systems, and offer controlling over drug-release by different triggers, such as light irradiation, pH variation, and temperature changes.