The production of W boson pairs in association with one jet in pp collisions at root 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 vertical bar eta vertical bar < 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 sigma(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 sigma(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 WWproduction with zero or one associated jet is reported. The measurements are compared to theoretical predictions and found in good agreement.