Biogenic polyamines, which play a role in DNA condensation and stabilization, are ubiquitous and are found at millimolar concentration in the nucleus of eukaryotic cells. The interaction modes of three polyamines—putrescine (Put), spermine (Spm), and spermidine (Spd)—with a self‐complementary 16 base pair (bp) duplex, are investigated by all‐atom explicit‐solvent molecular dynamics. The length of the amine aliphatic chain leads to a change of the interaction mode from minor groove binding to major groove binding. Through all‐atom dynamics, noncovalent interactions that stabilize the polyamine–DNA complex and prefigure the reactivity, leading to the low‐barrier formation of deleterious DNA–polyamine cross‐links, after one‐electron oxidation of a guanine nucleobase, are unraveled. The binding strength is quantified from the obtained trajectories by molecular mechanics generalized Born surface area post‐processing (MM‐GBSA). The values of binding free energies provide the same affinity order, Put<Spm<Spd, as that determined by recent isothermal calorimetry measurements, with a satisfactory correlation, to validate the structural predictions. The binding modes and carbon–nitrogen distances along the series of polyamines illustrate the selectivity towards deleterious DNA–polyamine cross‐link formation through the extraction of average approaching distances between the C8 atom of guanines and the ammonium group. These results imply that the formation of DNA–polyamine cross‐links involves deprotonation of the guanine radical cation to attack the polyamines, which must be positively charged to lie in the vicinity of the B‐helix.