A measurement of the rapidity and transverse momentum dependence of dijet azimuthal decorrelations is presented, using the quantity R-Delta phi. The quantity R-Delta phi specifies the fraction of the inclusive dijet events in which the azimuthal opening angle of the two jets with the highest transverse momenta is less than a given value of the parameter Delta phi(max). The quantity R-Delta phi is measured in proton-proton collisions at root s = 8 TeV as a function of the dijet rapidity interval, the event total scalar transverse momentum, and Delta phi(max). The measurement uses an event sample corresponding to an integrated luminosity of 20.2 fb(-1) collected with the ATLAS detector at the CERN Large Hadron Collider. Predictions of a perturbative QCD calculation at next-to-leading order in the strong coupling with corrections for nonperturbative effects are compared to the data. The theoretical predictions describe the data in the whole kinematic region. The data are used to determine the strong coupling alpha(S) and to study its running for momentum transfers from 260 GeV to above 1.6 TeV. Analysis that combines data at all momentum transfers results in alpha(S) (m(Z)) = 0.1127(- 0.0027) (+0.0063).