We developed a novel technique for the efficient conjugation of oligonucleotides with various alkyl azides such as fluorescent dyes, biotin, cholesterol, N-acetylgalactosamine (GalNAc), etc. using copper-catalysed alkyne-azide cycloaddition on the solid phase and CuI·P(OEt)3 as a catalyst. Conjugation is carried out in an oligonucleotide synthesizer in fully automated mode and is coupled to oligonucleotide synthesis and on-column deprotection. We also suggest a set of reagents for the construction of diverse conjugates. The sequential double-click procedure using a pentaerythritol-derived tetraazide followed by the addition of a GalNAc or Tris-GalNAc alkyne gives oligonucleotide-GalNAc dendrimer conjugates in good yields with minimal excess of sophisticated alkyne reagents. The approach is suitable for high-throughput synthesis of oligonucleotide conjugates ranging from fluorescent DNA probes to various multi-GalNAc derivatives of 2'-modified siRNA.