We report the direct measurement of the Be7 solar neutrino signal rate performed with the Borexino detector at the Laboratori Nazionali del Gran Sasso. The interaction rate of the 0.862MeV Be7 neutrinos is 49±3stat± 4systcounts/(day•100ton). The hypothesis of no oscillation for Be7 solar neutrinos is inconsistent with our measurement at the 4σ C.L. Our result is the first direct measurement of the survival probability for solar νe in the transition region between matter-enhanced and vacuum-driven oscillations. The measurement improves the experimental determination of the flux of Be7, pp, and CNO solar νe, and the limit on the effective neutrino magnetic moment using solar neutrinos.