Extracellular DNA, or eDNA, is recognised as a critical biofilm component; however, it is not understood how it forms networked matrix structures. Here, we isolate eDNA from static-culture Pseudomonas aeruginosa biofilms using ionic liquids to preserve its biophysical signatures of fluid viscoelasticity and the temperature dependency of DNA transitions. We describe a loss of eDNA network structure as resulting from a change in nucleic acid conformation, and propose that its ability to form viscoelastic structures is key to its role in building biofilm matrices. Solid-state analysis of isolated eDNA, as a proxy for eDNA structure in biofilms, reveals non-canonical Hoogsteen base pairs, triads or tetrads involving thymine or uracil, and guanine, suggesting that the eDNA forms G-quadruplex structures. These are less abundant in chromosomal DNA and disappear when eDNA undergoes conformation transition. We verify the occurrence of G-quadruplex structures in the extracellular matrix of intact static and flow-cell biofilms of P. aeruginosa, as displayed by the matrix to G-quadruplex-specific antibody binding, and validate the loss of G-quadruplex structures in vivo to occur coincident with the disappearance of eDNA fibres. Given their stability, understanding how extracellular G-quadruplex structures form will elucidate how P. aeruginosa eDNA builds viscoelastic networks, which are a foundational biofilm property.