Three of the transferring quartet are leaving the Orange as graduate transfers.
Dykes was 41-45 as a head coach at Louisiana Tech and Cal from 2010-16, replaces new Arkansas HC Chad Morris.
Bryan recorded six TFLs and four sacks in 2017.
Michigan may have just solved their quarterback problems in Ann Arbor, but it remains to be seen if Ole Miss transfer Shea Patterson will be eligible in 2018 or 2019.
Brandon Snyder spent the early Sunday morning hours in a county jail after being arrested for drunk driving.