Single-stranded DNA oligonucleotides have unique, and in some cases sequence-specific molecular interactions with the surface of carbon nanotubes that remain the subject of fundamental study. In this work, we observe and analyze a generic, ionic strength-mediated phase transition exhibited by over 25 distinct oligonucleotides adsorbed to single-walled carbon nanotubes (SWCNTs) in colloidal suspension. The phase transition occurs as monovalent salts are used to modify the ionic strength from 500 mM to 1 mM, causing a reversible reduction in the fluorescence quantum yield by as much as 90%. The phase transition is only observable by fluorescence quenching within a window of pH and in the presence of dissolved O-2, but occurs independently of this optical quenching. The negatively charged phosphate backbone increases (decreases) the DNA surface coverage on an areal basis at high (low) ionic strength, and is well described by a two-state equilibrium model. The resulting quantitative model is able to describe and link, for the first time, the observed changes in optical properties of DNA-wrapped SWCNTs with ionic strength, pH, adsorbed O-2, and ascorbic acid. Cytosine nucleobases are shown to alter the adhesion of the DNA to SWCNTs through direct protonation from solution, decreasing the driving force for this phase transition. We show that the phase transition also changes the observed SWCNT corona phase, modulating the recognition of riboflavin. These results provide insight into the unique molecular interactions between DNA and the SWCNT surface, and have implications for molecular sensing, assembly, and nanoparticle separations.