Eta Carinae is the colliding wind binary with the largest mass loss rate in our Galaxy and the only one in which hard X-ray emission has been detected. Eta Carinae is therefore a primary candidate to search for particle acceleration by probing its gamma-ray emission. We used the first 21 months of Fermi/LAT data to extract gamma-ray (0.2-100 GeV) images, spectra and light-curves, then combined them with multi-wavelength observations to model the non-thermal spectral energy distribution. A bright gamma-ray source is detected at the position of eta Carinae. Its flux at a few 100 MeV corresponds very well to the extrapolation of the hard X-ray spectrum towards higher energies. The spectral energy distribution features two distinct components. The first one extends over the keV to GeV energy range, and features an exponential cutoff at ~ 1 GeV. It can be understood as inverse Compton scattering of ultraviolet photons by electrons accelerated up to gamma~1E4 in the colliding wind region. The expected synchrotron emission is compatible with the existing upper limit on the non-thermal radio emission. The second component is a hard gamma-ray tail detected above 20 GeV. It could be explained by pi0-decay of accelerated hadrons interacting with the dense stellar wind. The ratio between the fluxes of the pi0 and inverse Compton components is roughly as predicted by simulations of colliding wind binaries. This hard gamma-ray tail can only be understood if emitted close to the wind collision region. The energy transferred to the accelerated particles (~5% of the collision mechanical energy) is comparable to that of the thermal X-ray emission. We have measured the electron spectrum responsible for the keV to GeV emission and detected an evidence of hadronic acceleration in eta Carinae. These observations are thus in good agreement with the colliding wind scenario suggested for eta Carinae.

7 pages, 5 figures