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The stability problem of grid-following inverters has been widely investigated. Nevertheless, existing literature has not yet proposed a strict stability analysis method for the overall grid-following inverter system with nonlinear nature. By focusing on single-phase systems and using frequency-domain nonlinear theory, this article proposes a universal absolute stability criterion for the single-phase grid-following inverters (SGFIs) equipped with orthogonal-normalization-based grid synchronizer. It will be shown that a SGFI will be absolutely stable under small- and large-disturbances if both the traditional impedance criterion and the synchronous nonlinear criterion are satisfied. The usefulness and applicability of the proposed new criterion are demonstrated by a case study of the conventional LCL-type SGFI system. Finally, the theoretical analysis is fully supported by a series of steady-state and transient experimental tests.