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 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 σ fid,1-jet WW = 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 σ fid,≤1-jet WW = 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 agreement.