DNA transposases facilitate genome rearrangements by moving DNA transposons around and between genomes by a cut-and-paste mechanism. DNA transposition proceeds in an ordered series of nucleoprotein complexes that coordinate pairing and cleavage of the transposon ends and integration of the cleaved ends at a new genomic site. Transposition is initiated by transposase recognition of the inverted repeat sequences marking each transposon end. Using a combination of solution scattering and biochemical techniques, we have determined the solution conformations and stoichiometries of DNA-free Mos1 transposase and of the transposase bound to a single transposon end. We show that Mos1 transposase is an elongated homodimer in the absence of DNA and that the N-terminal 55 residues, containing the first helix-turn-helix motif, are required for dimerization. This arrangement is remarkably different from the compact, crossed architecture of the dimer in the Mos1 paired-end complex (PEC). The transposase remains elongated when bound to a single-transposon end in a pre-cleavage complex, and the DNA is bound predominantly to one transposase monomer. We propose that a conformational change in the single-end complex, involving rotation of one half of the transposase along with binding of a second transposon end, could facilitate PEC assembly.