This paper details the solar neutrino analysis of the 385.17-day phase-III data set acquired by the Sudbury Neutrino Observatory (SNO). An array of 3He proportional counters was installed in the heavy-water target to measure precisely the rate of neutrino-deuteron neutral-current interactions. This technique to determine the total active 8B solar neutrino flux was largely independent of the methods employed in previous phases. The total flux of active neutrinos was measured to be 5.54+0.33−0.31(stat.)+0.36−0.34(syst.)×106 cm−2 s−1, consistent with previous measurements and standard solar models. A global analysis of solar and reactor neutrino mixing parameters yielded the best-fit values of Δm2=7.59+0.19−0.21×10−5eV2 and θ=34.4+1.3−1.2degrees.