Along with bright fluorescence in the near-IR range, heptamethine carbocyanine dyes possess affinity to cancer cells. Thus, these dyes could be utilized as fluorescent labels and vectors for drug delivery as covalent conjugates with cytotoxic compounds. To test the properties, structure-activity relationship, and scope of such conjugates, we synthesized drug-dye dyads of tricarbocyanine dyes with anthracycline drug daunorubicin. We used hydrophilic zwitterionic and hydrophobic positively charged benzoindoline-benzothiazole-based heptamethine dyes as terminal alkyne derivatives and N-acylated or oxime-linked daunorubicin as azido-derivatives. These two alkynes and two azides were coupled to each other by Cu-catalyzed Huisgen-Meldal-Sharpless cycloaddition (click reaction) to afford four conjugates. Molecules based on hydrophobic dyes possess submicromolar cytotoxicity to HCT116 cells. Cytotoxicity, cell penetration, intracellular distribution, apoptosis induction and the effect of antioxidants on toxicity were evaluated. The results show that the structure of the cyanine-anthracycline conjugate (hydrophilicity/hydrophobicity, charge, linker, attachment site) is important for its biological activity, thus, expansion of the chemical space of such conjugates could provide new molecular research tools for diagnostics and therapy.