This letter presents a memory-augmented system identifier with finite-time convergence for continuous-time uncertain nonlinear systems. A memory of events with significant effect on the performance of the identifier is formed, and reuse of historic data is leveraged in the identifier's update law to guarantee that the identifier's error converges to zero in finite time. An easy-to-check and verifiable metric defined on samples collected along the system's trajectories is provided to certify the finite-time convergence. The robustness of the proposed identifier to mismatched modeling error is analyzed. Finally, a simulation example verifies the efficiency of the proposed identifier.