We present a bijective characterization of suffix array permutations obtained from a characterization of Burrows-Wheeler arrays given in [1]. We show that previous characterizations [2], [3] and [4], or their analogs, can be obtained in a simple and elegant way using this relationship. To demonstrate the usefulness of our approach, we obtain simpler proofs for some known enumeration results about suffix arrays [3]. Our characterization of suffix arrays is the first based on their relationship with Burrows-Wheeler permutations.