Results are reported from a joint analysis of Phase I and Phase II data from the Sudbury Neutrino Observatory. The effective electron kinetic energy threshold used is T_eff=3.5 MeV, the lowest analysis threshold yet achieved with water Cherenkov detector data. In units of 10^6 cm^{-2} s^{-1}, the total flux of active-flavor neutrinos from 8B decay in the Sun measured using the neutral current (NC) reaction of neutrinos on deuterons, with no constraint on the 8B neutrino energy spectrum, is found to be Phi_NC = 5.140 ^{+0.160}_{-0.158} (stat) ^{+0.132}_{-0.117} (syst). These uncertainties are more than a factor of two smaller than previously published results. Also presented are the spectra of recoil electrons from the charged current reaction of neutrinos on deuterons and the elastic scattering of electrons. A fit to the SNO data in which the free parameters directly describe the total 8B neutrino flux and the energy-dependent nu_e survival probability provides a measure of the total 8B neutrino flux Phi_8B = 5.046 ^{+0.159}_{-0.152} (stat) ^{+0.107}_{-0.123} (syst). Combining these new results with results of all other solar experiments and the KamLAND reactor experiment yields best-fit values of the mixing parameters of theta_{12}=34.06 ^{+1.16}_{-0.84} degrees and Delta m^2_{21}=7.59 ^{+0.20}_{-0.21} x 10^{-5} eV^2. The global value of Phi_8B is extracted to a precision of ^{+2.38}_{-2.95} %. In a three-flavor analysis the best fit value of sin^2\theta_{13} is 2.00 ^{+2.09}_{-1.63} x 10^{-2}. Interpreting this as a limit implies an upper bound of sin^2\theta_{13}