6 pages, 4 figures ; We report the measurement of the 8B solar neutrinos interaction rate with the Borexino detector. The threshold energy of 2.8 MeV is the lowest for 8B achieved so far. The rate of 8B solar neutrino interaction as measured through their scattering on the target electrons is 0.26+-0.04(stat)+-0.02(syst) c/d/100 tons. This corresponds to an equivalent electron neutrino flux of (2.65+-0.44(stat)+-0.18(syst))x10^6 cm^-2 s^-1, as derived from the elastic scattering only, in good agreement with existing measurements and predictions. The corresponding 8B mean electron neutrino survival probability, assuming the BS07(GS98) Standard Solar Model, is 0.35+-0.10 at the effective energy of 8.6 MeV. The survival probability of the 0.862 MeV 7Be neutrinos was previously reported with a subset of these data as 0.56+-0.10. Eliminating the common sources of systematic errors, the ratio between the measured survival probabilities for 7Be and 8B neutrinos is 1.60+-0.33, 1.8 sigmas different form unity. For the first time we confirm, using data from a single detector, the presence of a transition between the low energy vacuum-driven and the high-energy matter-enhanced solar neutrino oscillations, in agreement with the prediction of the MSW-LMA solution for solar neutrinos.