The Sleeping Beauty (SB) transposon system is the leading and only DNA transposon-based gene-delivery vehicle that has been adapted for human gene therapy. The SB system consists of a transposon DNA flanked by inverted terminal repeats (ITRs) and a transposase enzyme that catalyzes gene transfer. SB DNA transposition, a cut-and-paste mechanism, occurs when two transposase enzymes bind to ITRs of transposon DNA and form a transpososome, in which the transposon DNA is integrated into the target DNA. The transposase enzyme is comprised of a DNA binding domain containing two subdomains, PAI and RED, and a catalytic domain. During transposition, SB transposase binds to different ITRs of the transposon DNA with different affinities, and this difference must be maintained for efficient transposition; however, the values of binding constants are not known. Here we use the PAI-H19Y mutant of the SB transposase as it is structurally stable at biologically relevant experimental conditions. Using several biophysical methods, such as microscale thermophoresis (MST), and nuclear magnetic resonance (NMR) spectroscopy, we were able to quantify the binding affinities of the PAI-H19Y mutant to transposon DNA.