In vitro viability assays against a representative panel of human cancer cell lines revealed that polyamines L1a and L5a displayed remarkable activity with IC50 values in the micromolar range. Preliminary research indicated that both compounds promoted G1 cell cycle arrest followed by cellular senescence and apoptosis. The induction of apoptotic cell death involved loss of mitochondrial outer membrane permeability and activation of caspases 3/7. Interestingly, L1a and L5a failed to activate cellular DNA damage response. The high intracellular zinc-chelating capacity of both compounds, deduced from the metal-specific Zinquin assay and ZnL2+ stability constant values in solution, strongly supports their cytotoxicity. These data along with quantum mechanical studies have enabled to establish a precise structure-activity relationship. Moreover, L1a and L5a showed appropriate drug-likeness by in silico methods. Based on these promising results, L1a and L5a should be considered a new class of zinc-chelating anticancer agents that deserves further development.