The QCD running coupling \alpha_s(Q^2) sets the strength of the interactions of quarks and gluons as a function of the momentum transfer Q. The Q^2 dependence of the coupling is required to describe hadronic interactions at both large and short distances. In this article we adopt the light-front holographic approach to strongly-coupled QCD, a formalism which incorporates confinement, predicts the spectroscopy of hadrons composed of light quarks, and describes the low-Q^2 analytic behavior of the strong coupling \alpha_s(Q^2). The high-Q^2 dependence of the coupling \alpha_s(Q^2) is specified by perturbative QCD and its renormalization group equation. The matching of the high and low Q^2 regimes of \alpha_s(Q^2) then determines the scale Q_0 which sets the interface between perturbative and nonperturbative hadron dynamics. The value of Q_0 can be used to set the factorization scale for DGLAP evolution of hadronic structure functions and the ERBL evolution of distribution amplitudes. We discuss the scheme-dependence of the value of Q_0 and the infrared fixed-point of the QCD coupling. Our analysis is carried out for the \bar{MS}, g_1, MOM and V renormalization schemes. Our results show that the discrepancies on the value of \alpha_s at large distance seen in the literature can be explained by different choices of renormalization schemes. We also provide the formulae to compute \alpha_s(Q^2) over the entire range of space-like momentum transfer for the different renormalization schemes discussed in this article. Show Partial Abstract