The method of B8 solar-neutrino measurement by means of the reaction eeee in the Kamiokande II detector is described in detail. A data sample of 1040 live detector days in the time period January 1987 through April 1990 yields a clear directional correlation of the solar-neutrino-induced electron events with respect to the Sun and a measurement of the differential electron energy distribution. The measured flux of B8 solar neutrinos from the subsamples of 450 days at electron energy threshold Ee9.3 MeV, and 590 days at Ee7.5 MeV relative to calculations of the B8 flux based on the standard solar model are 0.460.05(stat)0.06(syst) times the prediction of Bahcall and Ulrich, and 0.700.08(stat)0.09(syst) times the prediction of Turck-Chièze et al. The shape of the recoil electron energy distribution is consistent with that expected from the product of the known shape of the neutrino flux from B8 decay and the cross section for eeee scattering. Within the statistical error, there is no evidence in the solar-neutrino signal for a significant time variation.