Amphiphilic polymers with self-assembling abilities and stimuli-responsive functionalities have drawn significant interest as nanotransport systems for biomedical applications. In this study, we have designed and developed dual-stimuli-responsive multi-amphiphilic polymeric architectures using easily available biocompatible starting materials. We copolymerized poly(ethylene glycol) [bis(carboxymethyl) ether]diethylester (PEG-diester) and 3,3′-((2-azidopropane-1,3-diyl)bis(oxy))bis(propane-1,2-diol) (azido-triglycerol) using a biocatalyst, and the copolymer so obtained was grafted with azobenzene and polyglycerol dendron moieties to generate multi-amphiphilic polymeric architectures. The self-assembly and cargo encapsulation behaviors of the synthesized polymers were studied by encapsulating Nile red, a model hydrophobic probe. The controlled release of encapsulated Nile red was investigated by irradiation with UV light or exposure to lipase. The studied nanocarrier exhibited a slow release of Nile red, up to 72% in 10 days in the presence of lipase; however, only an insignificant release was observed in the absence of enzyme. Though the light induced release was found to proceed to a lesser extent, it was faster compared to lipase mediated release. Experimental data established the excellent capabilities of these systems as drug delivery nanocarriers by being non-cytotoxic up to a concentration of 500 μg/mL for 72 h. The cellular uptake study of the Nile red encapsulated polymers by confocal laser scanning microscopy suggested that such polymeric architectures may find potential applications as stimuli-responsive nanocarriers.