Ofir Minz-Manor in this article (Hebrew) writes on page 166 that, based on the nature of the poetry and particularly its lack of rhyme, the piyyut can be classified as having been written in the pre-Classical period (3rd - 5th centuries CE).
He notes further that this piyyut appears to be based on the description of the Kohein Gadol Shimon b. Yochanan which appears in Chapter 50 of the book of Ben Sira. (This identification was first made by Shir on page 225 of his Toldot.)
Unfortunately (as with many piyyutim from that long ago) the author's name does not seem to be known.