Oligonucleotide conjugates with boron clusters have found applications in different fields of molecular biology, biotechnology, and biomedicine as potential agents for boron neutron capture therapy, siRNA components, and antisense agents. Particularly, closo-dodecaborate anion represents a high-boron containing residue with remarkable chemical stability and low toxicity, suitable for the engineering of different constructs for biomedicine and molecular biology. In the present work, we synthesized novel oligonucleotide conjugates of closo-dodecaborate attached to the 5'-, 3'-, or both terminal positions of DNA, RNA, 2'-O-Me RNA, and 2'-F-Py RNA oligomers. For their synthesis, we employed click reaction with the azido derivative of closo-dodecaborate. The key physicochemical characteristics of the conjugates have been investigated using high-performance liquid chromatography, gel electrophoresis, UV thermal melting, and circular dichroism spectroscopy. Incorporation of closo-dodecaborate residues at the 3'-end of all oligomers stabilized their complementary complexes, while analogous 5'-modification decreased duplex stability. Two boron clusters attached to the opposite ends of the oligomer only slightly influence the stability of complementary complexes of RNA oligonucleotide and its 2'-O-methyl and 2'-fluoro analogs. On the contrary, the same modification of DNA oligonucleotides significantly destabilized DNA/DNA duplex but gave a strong stabilization of the duplex with RNA target. According to CD spectroscopy results, two terminal closo-dodecaborate residues cause a prominent structural rearrangement of complementary complexes with a substantial shift from B-form to the A-form of the double helix. The revealed changes of key characteristics of oligonucleotides caused by incorporation of terminal boron clusters, such as the increase of hydrophobicity, change of duplex stability, and prominent structural changes for DNA conjugates, should be taken into account for the development of antisense oligonucleotides, siRNAs, or aptamers bearing boron clusters. These features may also be used for engineering of developing NA constructs with pre-defined properties.