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 (3.69 +/- 0.16) x 10(31) proton x year after all selection cuts and background subtraction, we detected (14.3 +/- 4.4) geo-neutrino events assuming a fixed chondritic mass Th/U ratio of 3.9. This corresponds to a geo-neutrino signal S-geo = (38.8 +/- 12.0) TNU with just a 6 x 10(-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 = (10.6 +/- 12.7) TNU and S-U = (26.5 +/- 19.5) TNU. Borexino data alone are compatible with a mantle geo-neutrino signal of (15.4 +/- 12.3) TNU, while a combined analysis with the KamLAND data allows to extract a mantle signal of (14.1 +/-. 8.1) 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. (c) 2013 Elsevier B.V. All rights reserved.