This work investigates perfectly covert communication assisted by a passive Intelligent Reflecting Surface (IRS). In contrast to most existing IRS-assisted covert communication studies, which allow a nonzero detection leakage and optimize an epsilon-covertness constraint, we study the stricter regime in which the received signal component at the warden is completely canceled. We first derive a necessary and sufficient condition for perfect covertness and characterize its feasibility under Rayleigh fading. For the case of two reflecting elements, we provide a closed-form characterization of all feasible IRS phase configurations. For a general number of reflecting elements, we prove that the perfect-covertness condition is eventually satisfied almost surely as the number of IRS elements grows. To construct such configurations, we distinguish between the full Bob-aware design problem and the perfect-covertness feasibility subproblem, and formulate the latter as a warden-signal nulling problem. We then propose a gradient-based IRS phase-design algorithm with per-iteration computational complexity $O(N)$ and prove that, with random initialization, it converges to a global minimizer with probability one over the initialization set. The numerical results show that Bob-aware initialization preserves the legitimate link while driving Willie leakage to the numerical floor, and further evaluate multi-antenna Willie and imperfect-CSI settings. Finally, to address practical limitations such as imperfect channel state information and finite detector resolution, we introduce operational perfect covertness and derive a robust transmit-power condition that guarantees indistinguishability at the warden under bounded CSI uncertainty.

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