ATLAS has measured two-particle correlations as a function of the relative azimuthal angle, Δφ, and pseudorapidity, Δη, in s=13 and 2.76 TeV pp collisions at the LHC using charged particles measured in the pseudorapidity interval |η|<2.5. The correlation functions evaluated in different intervals of measured charged-particle multiplicity show a multiplicity-dependent enhancement at Δφ∼0 that extends over a wide range of Δη, which has been referred to as the "ridge." Per-trigger-particle yields, Y(Δφ), are measured over 2<|Δη|<5. For both collision energies, the Y(Δφ) distribution in all multiplicity intervals is found to be consistent with a linear combination of the per-trigger-particle yields measured in collisions with less than 20 reconstructed tracks, and a constant combinatoric contribution modulated by cos(2Δφ). The fitted Fourier coefficient, v2,2, exhibits factorization, suggesting that the ridge results from per-event cos(2φ) modulation of the single-particle distribution with Fourier coefficients v2. The v2 values are presented as a function of multiplicity and transverse momentum. They are found to be approximately constant as a function of multiplicity and to have a pT dependence similar to that measured in p+Pb and Pb+Pb collisions. The v2 values in the 13 and 2.76 TeV data are consistent within uncertainties. These results suggest that the ridge in pp collisions arises from the same or similar underlying physics as observed in p+Pb collisions, and that the dynamics responsible for the ridge has no strong s dependence.