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 $pm$ 0.16) $times$ $10^{31}$ proton $times$ year after all selection cuts and background subtraction, we detected (14.3 $pm$ 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 $pm$ 12.0) TNU with just a 6 $times$ $10^{-6}$ probability for a null geo-neutrino measurement. With U and Th left as free parameters in the fit, the relative signals are $S_{mathrm{Th}}$ = (10.6 $pm$ 12.7) TNU and $S_mathrm{U}$ = (26.5 $pm$ 19.5) TNU. Borexino data alone are compatible with a mantle geo--neutrino signal of (15.4 $pm$ 12.3) TNU, while a combined analysis with the KamLAND data allows to extract a mantle signal of (14.1 $pm$ 8.1) TNU. Our measurement of a reactor anti--neutrino signal $S_{react}$ = 84.5$^{+19.3}_{-18.9}$ TNU is in agreement with expectations in the presence of neutrino oscillations.
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