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Online assessment of transient stability of power systems is critical for avoiding blackout. The increasing installation of phasor measurement units in power systems and the advancement of the wide-area measurement systems make it possible to develop methods for online assessment of power systems by using a large amount of real-time synchronous data. In this paper, we propose an approach based on the largest Lyapunov exponent (LLE) for online transient rotor angle stability assessment, using only wide-area measurement systems data. Through establishing a mathematical model that accounts for the LLE value and the rotor speed, as well as analyzing the post-fault phase-plane trajectory, we present a fast stability criterion to determine whether transient instability occurs. The proposed approach is model-free and does not need long-time LLE data to identify the final sign of the LLE. Furthermore, to reduce computational cost and realize online assessment for large-scale power systems, the critical generator pair (CGP) is recognized as the observation for the rotor angle stability assessment, and an effective algorithm for identifying the CGP is presented. Several case studies on the IEEE-39 bus test system and East China power grid are reported to demonstrate the accuracy and effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]