The rate of neutrino-electron elastic scattering interactions from 862 keV (7)Be solar neutrinos in Borexino is determined to be 46.0±1.5(stat)(-1.6)(+1.5)(syst) counts/(day·100 ton). This corresponds to a ν(e)-equivalent (7)Be solar neutrino flux of (3.10±0.15)×10(9) cm(-2) s(-1) and, under the assumption of ν(e) transition to other active neutrino flavours, yields an electron neutrino survival probability of 0.51±0.07 at 862 keV. The no flavor change hypothesis is ruled out at 5.0 σ. A global solar neutrino analysis with free fluxes determines Φ(pp)=6.06(-0.06)(+0.02)×10(10) cm(-2) s(-1) and Φ(CNO)<1.3×10(9) cm(-2) s(-1) (95% C.L.). These results significantly improve the precision with which the Mikheyev-Smirnov-Wolfenstein large mixing angle neutrino oscillation model is experimentally tested at low energy.