We report measurements of the exclusive electroproduction of K+Λ and K+Σ0 final states from a proton target using the Continuous Electron Beam Accelerator Facility (CEBAF) large-acceptance spectrometer (CLAS) detector at the Thomas Jefferson National Accelerator Facility. The separated structure functions σT,σL,σTT, and σLT were extracted from the Φ- and ε-dependent differential cross sections taken with electron beam energies of 2.567, 4.056, and 4.247 GeV. This analysis represents the first σL/σT separation with the CLAS detector, and the first measurement of the kaon electroproduction structure functions away from parallel kinematics. The data span a broad range of momentum transfers from 0.5