A new monophosphine Cu(I) complex bearing bis(pyrazolyl)methane (L1) (CuIL1PPh3) was synthesized and used as a catalyst for the three-component click reaction from an alkyl halide, sodium azide, and terminal alkyne to furnish 1,4-disubstituted 1,2,3-triazoles in up to 93% yield. The catalyst is highly stable, compatible with oxygen/water, and works with total efficiency under ultrasonic condition. The structure of the complex was studied and confirmed by X-ray crystallography, finding a riveting relationship with its catalytic activity. This sustainable triazoles synthesis is distinguished by its high atom economy, low catalyst loading (up to 0.5 mol %), broad substrate scope, short reaction times, operational simplicity, and an easy gram-scale supply of a functionalized product for subsequent synthetic applications.