Jets are identified and their properties studied in center-of-mass energy sqrt(s) = 7 TeV proton-proton collisions at the Large Hadron Collider using charged particles measured by the ATLAS inner detector. Events are selected using a minimum bias trigger, allowing jets at very low transverse momentum to be observed and their characteristics in the transition to high-momentum fully perturbative jets to be studied. Jets are reconstructed using the anti-k(t) algorithm applied to charged particles with two radius parameter choices, 0.4 and 0.6. An inclusive charged jet transverse momentum cross section measurement from 4 GeV to 100 GeV is shown for four ranges in rapidity extending to 1.9 and corrected to charged particle-level truth jets. The transverse momenta and longitudinal momentum fractions of charged particles within jets are measured, along with the charged particle multiplicity and the particle density as a function of radial distance from the jet axis. Comparison of the data with the theoretical models implemented in existing tunings of Monte Carlo event generators indicates reasonable overall agreement between data and Monte Carlo. These comparisons are sensitive to Monte Carlo parton showering, hadronization, and soft physics models.