We present a measurement of the geo-neutrino signal obtained from 1353 days of data with the Borexino detector at Laboratori Nazionali del Gran Sasso in Italy. With a fiducial exposure of \left ( 3.69± 0.16 \right )x10^{31} proton × year after all selection cuts and background subtraction, we detected \left ( 14.3± 4.4 \right ) geo-neutrino events assuming a fixed chondritic mass Th/U ratio of 3.9. This corresponds to a geo-neutrino signal S_geo = \left ( 38.8± 12.0 \right ) TNU with just a 6x10^{-6} probability for a null geo-neutrino measurement. With U and Th left as free parameters in the fit, the relative signals are S_{Th}= \left ( 10.6± 12.7 \right ) TNU and S_{U}= \left ( 26.5± 19.5 \right ) TNU. Borexino data alone are compatible with a mantle geo-neutrino signal of \left ( 15.4± 12.3 \right ) TNU, while a combined analysis with the KamLAND data allows to extract a mantle signal of \left ( 14.1± 8.1 \right ) TNU. Our measurement of 31.2_{-6.1}^{+7.0} reactor anti-neutrino events is in agreement with expectations in the presence of neutrino oscillations.