We report experimental details and results of a new measurement of the decay K+→π+π-e+νe(Ke4). A sample of more than 400,000 Ke4 events with low background has been collected by Experiment 865 at the Brookhaven Alternate Gradient Synchrotron. From these data, the branching ratio (4.11±0.01±0.11)×10-5 and the ππ invariant mass dependence of the form factors F, G, and H of the weak hadronic current as well as the phase shift difference δ00-δ11 for ππ scattering were extracted. Using constraints based on analyticity and chiral symmetry, a new value with considerably improved accuracy for the s-wave ππ scattering length a00 has been obtained also: a00=0.216±0.013 (stat)±0.002 (syst)±0.002 (theor).