We report on gamma-ray analysis of the region containing the bright TeV source HESS J1640-465 and the close-by TeV source HESS J1641 -463 using 64 months of observations with the Fermi Large Area Telescope (LAT). Previously only one GeV source was reported in this region and was associated with HESS J1640-465. With an increased data set and the improved sensitivity afforded by the reprocessed data (P7REP) of the LAT, we now report the detection, morphological study, and spectral analysis of two distinct sources above 100 MeV. The softest emission in this region comes from the TeV source HESS J1641-463 which is well fitted with a power law of index Gamma = 2.47 0.05 0.06 and presents no significant gamma-ray signal above 10 GeV, which contrasts with its hard spectrum at TeV energies. The Fermi-LAT spectrum of the second TeV source, HESS J1640-465 is well described by a power-law shape of index Gamma = 1.99 0.04 0.07 that links up naturally with the spectral data points obtained by the High Energy Stereoscopic System (H.E.S.S.). These new results provide new constraints concerning the identification of these two puzzling y-ray sources