A set of Cu(I) complexes with 3,7-diacetyl-1,3,7-triaza-5-phosphabicyclo-[3.3.1]nonane (DAPTA) phosphine ligands viz. [CuX(κP-DAPTA)3] (1: X = Br; 2: X = I) and [Cu(μ-X)(κP-DAPTA)2]2 (3: X = Br; 4: X = I) were immobilized on activated carbon (AC) and multi-walled carbon nanotubes (CNT), as well as on these materials after surface functionalization. The immobilized copper(I) complexes have shown favorable catalytic activity for the one-pot, microwave-assisted synthesis of 1,2,3-triazoles via the azide-alkyne cycloaddition reaction (CuAAC). The heterogenized systems with a copper loading of only 1.5–1.6% (w/w relative to carbon), established quantitative conversions after 15 min, at 80 °C, using 0.5 mol% of catalyst loading (relative to benzyl bromide). The most efficient supports concerning heterogenization were CNT treated with nitric acid and NaOH, and involving complexes 2 and 4 (in the same order, 2_CNT-ox-Na and 4_CNT-ox-Na). The immobilized catalysts can be recovered and recycled by simple workup and reused up to four consecutive cycles although with loss of activity.