The properties of jets produced in p+p collisions at √s=200GeV are measured using the method of two-particle correlations. The trigger particle is a leading particle from a large transverse momentum jet while the associated particle comes from either the same jet or the away-side jet. Analysis of the angular width of the near-side peak in the correlation function determines the jet-fragmentation transverse momentum jT. The extracted value, √〈jT2〉 =585±6(stat)±15(sys)MeV/c, is constant with respect to the trigger particle transverse momentum, and comparable to the previous lower √s measurements. The width of the away-side peak is shown to be a convolution of jT with the fragmentation variable, z, and the partonic transverse momentum, kT. The 〈z〉 is determined through a combined analysis of the measured π0 inclusive and associated spectra using jet-fragmentation functions measured in e+e- collisions. The final extracted values of kT are then determined to also be independent of the trigger particle transverse momentum, over the range measured, with value of √〈kT2〉 =2.68±0.07(stat)±0.34(sys)GeV/c.