The production of W boson pairs in association with one jet in pp collisions at s=8 TeV is studied using data corresponding to an integrated luminosity of 20.3 fb −1 collected by the ATLAS detector during 2012 at the CERN Large Hadron Collider. The cross section is measured in a fiducial phase-space region defined by the presence of exactly one electron and one muon, missing transverse momentum and exactly one jet with a transverse momentum above 25 GeV and a pseudorapidity of |η|<4.5 . The leptons are required to have opposite electric charge and to pass transverse momentum and pseudorapidity requirements. The fiducial cross section is found to be σWWfid,1-jet=136±6(stat)±14(syst)±3(lumi) fb . In combination with a previous measurement restricted to leptonic final states with no associated jets, the fiducial cross section of WW production with zero or one jet is measured to be σWWfid,≤1-jet=511±9(stat)±26(syst)±10(lumi) fb . The ratio of fiducial cross sections in final states with one and zero jets is determined to be 0.36±0.05 . Finally, a total cross section extrapolated from the fiducial measurement of WW production with zero or one associated jet is reported. The measurements are compared to theoretical predictions and found in good