The fabrication of stable fluorescent copper nanoclusters (CuNCs) in aqueous media is still challenging, despite the low price and potential biomedical applications. Herein, we report a facile and efficient strategy for assembling CuNCs using multifunctional thiolated copolymers with pH and thermoresponsive features. The new nanohybrids are formed via a simple one-pot approach through the reduction of a copper salt with hydrazine in the presence of a multithiolated polymer, which provides a template during nanocluster assembly and further efficient protection against oxidation and aggregation. Furthermore, the thermo- and pH-responsive properties of the pristine copolymers endow the nanohybrids with these stimuli-responsive features. The thiol content and the macromolecular size of the polymer ligands exert strong influences on the final photophysical properties of these new hybrid luminescent nanoclusters. The existence of stable bright greenish-yellow emission in water over long periods of time, the high photostability under UV irradiation and the strong oxidation resistance toward hydrogen peroxide of the hybrid CuNCs suggest that they have great promise for nanomedicine, bioassay and nanosensor use. Furthermore, the polymeric CuNCs obtained have been successfully tested as optical switch-off sensors for the sensitive and highly selective detection of Hg²⁺ in the presence of other metal ions in liquid and solid states. Finally, we demonstrate the practical application of the new hybrid to Hg²⁺ detection in human urine.