The differential charged jet cross sections, jet fragmentation distributions, and jet shapes are measured in minimum bias proton-proton collisions at center-of-mass energy root s = 7 TeV using the ALICE detector at the LHC. Jets are reconstructed from charged particle momenta in the midrapidity region using the sequential recombination k(T) and anti-k(T) as well as the SISCone jet finding algorithms with several resolution parameters in the range R = 0.2-0.6. Differential jet production cross sections measured with the three jet finders are in agreement in the transverse momentum (p(T)) interval 20 <p(T)(jet,ch) <100 GeV/c. They are also consistent with prior measurements carried out at the LHC by the ATLAS Collaboration. The jet charged particle multiplicity rises monotonically with increasing jet p(T), in qualitative agreement with prior observations at lower energies. The transverse profiles of leading jets are investigated using radial momentum density distributions as well as distributions of the avera