Guanine-rich DNA/RNA sequences can form Hoogsteen bonds to adopt noncanonical secondary structures called G-quadruplexes, and these have been associated with diverse cellular processes. There has been considerable research interest in the design of G4-interacting ligands for cellular probing of the G4 structure and understanding its associated biological function. Most of the fluorescent G4 ligands either do not have significant selectivity over other nucleic acid structures, have high Stokes shift, or are not in the near-infrared (NIR) region, which limits its cellular visualization. The current work involves the rational design and synthesis of NIR fluorescent probes comprising a (Z)-1-methyl-2-((3-methylbenzo[d]thiazol-2(3H)-ylidene)methyl)quinolin-1-ium scaffold. Among the designed molecules, 4a exhibited far-red fluorescence (λmax = 680 nm) with large Stokes shift (∼182 nm) upon selective binding to human telomeric G-quadruplexes. The dye 4a does not disturb the conformation and stability of G-quadruplexes, thereby making it suitable for nucleic acid research based applications. Interestingly, 4a showed remarkable selectivity over single- and double-stranded structures in contrast to a commercially available quadruplex binding probe, Thiazole orange (TO). The molecular docking studies indicate that 4a binds at the groove region of the telomeric DNA G-quadruplex through π-π stacking interactions with the quinoline and amine-substituted phenyl ring and with the phosphate backbone through anion-π interactions with the benzothiazole ring. The designed molecule 4a has interesting photophysical properties, cell permeability, and biocompatibility with minimal cytotoxicity. Fluorescence imaging studies in live HeLa cells showed that probe 4a binds to the transient population of the DNA G-quadruplex in the nucleus and RNA quadruplexes in the cytoplasm. In brief, G-quadruplex NIR fluorescent probe 4a with a higher signal/noise ratio has significant potential for cellular imaging studies and thus opens avenues to decipher the biological pathways for better understanding of G-quadruplex biology.