The first-in-class luminescent dinucleoside phosphate analogs with a [Re2(μ-Cl)2(CO)6(μ-pyridazine)] "click" linker as a replacement for the natural phosphate group are reported together with the synthesis of luminescent adenosine and thymidine derivatives having the [Re2(μ-Cl)2(CO)6(μ-pyridazine)] entity attached to positions 5' and 3', respectively. These compounds were synthesized by applying inverse-electron-demand Diels-Alder and copper(I)-catalyzed azide-alkyne 1,3-dipolar cycloaddition reactions in three or four steps. The obtained compounds exhibited orange emission (λPL ≈ 600 nm, ΦPL ≈ 0.10, and τ = 0.33-0.61 μs) and no toxicity (except for one nucleoside) to human HeLa cervical epithelioid and Ishikawa endometrial adenocarcinoma cancer cells in vitro. Furthermore, the compounds' ability to inhibit the growth of Gram-positive Staphylococcus aureus and Gram-negative Escherichia coli bacterial strains was moderate and only observed at a high concentration of 100 μM. Confocal microscopy imaging revealed that the "dirhenium carbonyl" dinucleosides and nucleosides localized mainly in the membranous structures of HeLa cells and uniformly inside S. aureus and E. coli bacterial cells. An interesting finding was that some of the tested compounds were also found in the nuclei of HeLa cells.