Results are presented on the production of jets of particles in association with a $Z/{\ensuremath{\gamma}}^{*}$ boson, in proton-proton collisions at $\sqrt{s}=7\text{ }\text{ }\mathrm{TeV}$ with the ATLAS detector. The analysis includes the full 2010 data set, collected with a low rate of multiple proton-proton collisions in the accelerator, corresponding to an integrated luminosity of $36\text{ }\text{ }{\mathrm{pb}}^{\ensuremath{-}1}$. Inclusive jet cross sections in $Z/{\ensuremath{\gamma}}^{*}$ events, with $Z/{\ensuremath{\gamma}}^{*}$ decaying into electron or muon pairs, are measured for jets with transverse momentum ${p}_{T}>30\text{ }\text{ }\mathrm{GeV}$ and jet rapidity $|y|<4.4$. The measurements are compared to next-to-leading-order perturbative QCD calculations, and to predictions from different Monte Carlo generators implementing leading-order matrix elements supplemented by parton showers.