Copper(I) [Cu₂(μ-Br)₂(^tBuImCH₂pyCH₂L)] _n (L = OMe, NEt₂, NH^tBu) compounds supported by flexible functionalized NHC-based polydentate ligands have been prepared in a one-pot procedure by reacting the corresponding imidazolium salt with an excess of copper powder and Ag₂O. An X-ray diffraction analysis has revealed that [Cu₂(μ-Br)₂(^tBuImCH₂pyCH₂NEt₂)] _n is a linear coordination polymer formed by bimetallic [Cu(μ-Br)]₂ units linked by the lutidine-based NHC-py-NEt₂ ligand, which acts as a heteroditopic ligand with a 1κC-2κ² N,N' coordination mode. We propose that the polymeric compounds break down in the solution into more compact tetranuclear [Cu₂(μ-Br)₂(^tBuImCH₂pyCH₂L)]₂ compounds with a coordination mode identical to the functionalized NHC ligands. These compounds have been found to exhibit high catalytic activity in the Cu-catalyzed azide-alkyne cycloaddition (CuAAC) reaction. In particular, [Cu₂(μ-Br)₂(^tBuImCH₂pyCH₂NEt₂)]₂ efficiently catalyzes the click reaction of a range of azides and alkynes, under an inert atmosphere at room temperature in neat conditions at a very low catalyst loading, to quantitatively afford the corresponding 1,4-disubstituted 1,2,3-triazole derivatives in a few minutes. The cycloaddition reaction of benzyl azide to phenylacetylene can be performed at 25-50 ppm catalyst loading by increasing the reaction time and/or temperature. Reactivity studies have shown that the activation of the polynuclear catalyst precursor involves the alkyne deprotonation by the NHC moiety of the polydentate ligand to afford a copper(I)-alkynyl species bearing a functionalized imidazolium ligand. DFT calculations support the participation of the dinuclear species [(CuBr)₂(μ-^tBuImCH₂pyCH₂NEt₂)], resulting from the fragmentation of the tetranuclear compound, as the catalytically active species. The proposed reaction pathway proceeds through zwitterionic dinuclear intermediates and entails the active participation of both copper atoms, as well as the NHC moiety as an internal base, which activates the reacting alkyne via deprotonation.