Seven conjugates composed of well-known fluoroquinolone antibacterial agents, ciprofloxacin (CIP) or levofloxacin (LVX), and a cell-penetrating peptide transportan 10 (TP10-NH2) were synthesised. The drugs were covalently bound to the peptide via an amide bond, methylenecarbonyl moiety, or a disulfide bridge. Conjugation of fluoroquinolones to TP10-NH2 resulted in congeners demonstrating antifungal in vitro activity against human pathogenic yeasts of the Candida genus (MICs in the 6.25–100 µM range), whereas the components were poorly active. The antibacterial in vitro activity of most of the conjugates was lower than the activity of CIP or LVX, but the antibacterial effect of CIP-S-S-TP10-NH2 was similar to the mother fluoroquinolone. Additionally, for two representative CIP and LVX conjugates, a rapid bactericidal effect was shown. Compared to fluoroquinolones, TP10-NH2 and the majority of its conjugates generated a relatively low level of reactive oxygen species (ROS) in human embryonic kidney cells (HEK293) and human myeloid leukemia cells (HL-60). The conjugates exhibited cytotoxicity against three cell lines, HEK293, HepG2 (human liver cancer cell line), and LLC-PK1 (old male pig kidney cells), with IC50 values in the 10–100 µM range and hemolytic activity. The mammalian toxicity was due to the intrinsic cytoplasmic membrane disruption activity of TP10-NH2 since fluoroquinolones themselves were not cytotoxic. Nevertheless, the selectivity index values of the conjugates, both for the bacteria and human pathogenic yeasts, remained favourable.