Cutcliffe led the Blue Devils to a 10-4 season that included their first appearance in the ACC title game as well as the Chick-fil-A Bowl.
Bohl, who left North Dakota State for Wyoming, led the Bison to their third straight FCS national championship.
Adam Dorrell won the Division II award after leading Northwest Missouri State to a 15-0 record and the national title.
Lance Leipold of Wisconsin-Whitewater was the coach of the year in Division III. The Warhawks went unbeaten and won a fifth Division III national title. Mike Woodley won for NAIA after leading Grand View to its first national title.