In this paper, we derive the closed form expression of the Error Vector magnitude (EVM) of Orthogonal Frequency Division Multiplexing (OFDM) signals for optimal Tone Reservation (TR) Peak to Average Power Ratio (PAPR) reduction. This expression is the theoretical lower bound of the EVM that is affordable through TR PAPR reduction. It considers the High Power Amplifier (HPA) non-linearities and memory effects. The provided EVM expression essentially relies on the probability distribution of the time domain amplitude after applying TR algorithm. The proposed methodology consists in first evaluating such distribution, and then integrating it to get the EVM. It has been applied here in the case of the optimal TR PAPR reduction algorithm but can be extended to other TR algorithms given that the time domain amplitude distribution can be extracted. Hence, this paper provides a general analytical framework applicable for any TR algorithm. © 2020 IEEE.