Inclusive jet and dijet cross sections have been measured in proton-proton collisions at a center-of-mass energy of 7 TeV using the ATLAS detector at the Large Hadron Collider. The cross sections were measured using jets clustered with the anti-${k}_{t}$ algorithm with parameters $R=0.4$ and $R=0.6$. These measurements are based on the 2010 data sample, consisting of a total integrated luminosity of $37\text{ }\text{ }{\mathrm{pb}}^{\ensuremath{-}1}$. Inclusive jet double-differential cross sections are presented as a function of jet transverse momentum, in bins of jet rapidity. Dijet double-differential cross sections are studied as a function of the dijet invariant mass, in bins of half the rapidity separation of the two leading jets. The measurements are performed in the jet rapidity range $|y|<4.4$, covering jet transverse momenta from 20 GeV to 1.5 TeV and dijet invariant masses from 70 GeV to 5 TeV. The data are compared to expectations based on next-to-leading-order QCD calculations corrected for nonperturbative effects, as well as to next-to-leading-order Monte Carlo predictions. In addition to a test of the theory in a new kinematic regime, the data also provide sensitivity to parton distribution functions in a region where they are currently not well-constrained.