This article delves into the predefined-time output-feedback leader-following consensus problem of uncertain pure-feedback nonlinear multiagent systems for the first time. To streamline subsequent design, the original systems in pure-feedback form are first transformed into canonical systems. Following this, a distributed predefined-time extended state observer (ESO) and a local predefined-time ESO are developed to reconstruct the unknown states/lumped disturbance of the transformed leader system and follower systems, respectively. Based on the estimated states and utilizing a bounded regulation function, two nonsingular and nonconservative predefined-time control laws are formulated to achieve consensus tracking. The proposed method showcases the following advantages: 1) the actual convergence time rather than the upper bound of the convergence time (UBCT) of the tracking errors can be explicitly specified a priori regardless of the initial conditions in a bounded region, optimizing control energy usage and 2) the system overshoot could be effectively reduced by selecting appropriate parameters for the regulation function. Finally, numerical examples are conducted to verify the obtained results.