The preparation of novel phosphinite- and phosphonite-bearing copper(I) complexes of the general formula [CuX(L)] is reported. These compounds, which remain scarce in the literature, could be prepared using readily available starting materials and were spectroscopically and structurally characterized. These complexes, together with their known phosphine and phosphite analogues, were then applied to the 1,3-dipolar cycloaddition of azides and alkynes, to find that the new complexes displayed the best activities. Full optimization of the reaction conditions resulted in a noteworthy Click catalytic system, active under very mild reaction conditions in the absence of any additive and using low metal loadings.