This paper is concerned with the strategy consensus of n-person random evolutionary Boolean games with time delay (REBGTD). To begin with, we present the model of n-person REBGTD and derive its algebraic form via the semi-tensor product (STP) of matrices. Subsequently, based on a series of stochastic reachable sets and control invariant subsets, the strategy consensus problem of n-person REBGTD is transformed into the set stabilization problem of equivalent systems, and a necessary and sufficient condition is proposed for the strategy consensus with probability one of n-person REBGTD. Moreover, the state feedback controllers are designed to realize the strategy consensus of n-person REBGTD. Finally, to validate the theoretical results, an illustrative example is presented at the end of the paper.