Measurements of transverse energy-energy correlations and their associated asymmetries in multi-jet events using the ATLAS detector at the LHC are presented. The data used correspond to vs = 8 TeV proton-proton collisions with an integrated luminosity of 20.2 fb(-1). The results are presented in bins of the scalar sum of the transverse momenta of the two leading jets, unfolded to the particle level and compared to the predictions from Monte Carlo simulations. A comparison with next-to-leading-order perturbative QCD is also performed, showing excellent agreement within the uncertainties. From this comparison, the value of the strong coupling constant is extracted for different energy regimes, thus testing the running of alpha(s)(mu) predicted in QCD up to scales over 1 TeV. A global fit to the transverse energy-energy correlation distributions yields alpha(s)(m(Z)) = 0.1162 +/- 0.0011 (exp.)(-0.0070)(+0.0084) (theo.), while a global fit to the asymmetry distributions yields a value of alpha(s)(m(Z)) = 0.1196 +/- 0.0013 (exp.)(-0.0045)(+0.0075) (theo.).