We present a measurement of two-particle angular correlations in proton-proton collisions at root s = 900 GeV and 7 TeV. The collision events were collected during 2009 and 2010 with the ATLAS detector at the Large Hadron Collider using a single-arm minimum bias trigger. Correlations are measured for charged particles produced in the kinematic range of transverse momentum p(T) > 100 MeV and pseudorapidity vertical bar eta vertical bar < 2.5. A complex structure in pseudorapidity and azimuth is observed at both collision energies. Results are compared to PYTHIA 8 and HERWIG++ as well as to the AMBT2B, DW and Perugia 2011 tunes of PYTHIA 6. The data are not satisfactorily described by any of these models.