We use the recently reported KamLAND measurements on oscillations of reactor anti-neutrinos, together with the data of previously reported solar neutrino experiments, to show that: (1) the total B-8 neutrino flux emitted by the Sun is 1.00 (1 +/- 0.06) (1sigma) of the standard solar model (BP00) predicted flux, (2) the KamLAND measurements reduce the area of the globally allowed oscillation regions that must be explored in model fitting by six orders of magnitude in the Deltam(2-)tan(2) theta plane, (3) LMA is now the unique oscillation solution to a CL of 4.7sigma, (4) maximal mixing is disfavored at 3.1sigma, (5) active-sterile admixtures are constrained to sin(2) eta less than or equal to 0.13 at 1sigma, (6) the observed B-8 flux that is in the form of sterile neutrinos is 0.00(-0.00)(+0.09) (1sigma), of the standard solar model (BP00) predicted flux, and (7) non-standard solar models that were invented to avoid completely solar neutrino oscillations are excluded by KamLAND plus solar data at 7.9sigma. We also refine quantitative predictions for future Be-7 and p - p solar neutrino experiments.