Abstract : We announce the discovery of 1-100 GeV gamma-ray emission from the archetypal TeV pulsar wind nebula (PWN) HESS J1825−137 using 20 months of survey data from the Fermi-Large Area Telescope (LAT). The gamma-ray emission detected by the LAT is significantly spatially extended, with a best-fit rms extension of σ = 0. ◦ 56±0. ◦ 07 for an assumed Gaussian model. The 1-100 GeV LAT spectrum of this source is well described by a power law with a spectral index of 1.38 ± 0.12 ± 0.16 and an integral flux above 1 GeV of (6.50 ± 0.21 ± 3.90) ×10−9 cm−2 s−1. The first errors represent the statistical errors on the fit parameters, while the second ones are the systematic uncertainties. Detailed morphological and spectral analyses bring new constraints on the energetics and magnetic field of the PWN system. The spatial extent and hard spectrum of the GeV emission are consistent with the picture of an inverse Compton origin of the GeV-TeV emission in a cooling-limited nebula powered by the pulsar PSR J1826−1334
