Eight former coach of the year winners attended the announcement: Bill Curry, Fisher DeBerry, Vince Dooley, Ralph Friedgen, Fred Goldsmith, Jim Grobe, Ken Hatfield and Dick Sheridan.
"There are a lot of great parts of this," Cutcliffe said. "I would have to say the greatest part is being on stage with men like these coaches.
"This is the most meaningful thing that has happened to me. When these gentlemen walked into the room, the meaning of the Bobby Dodd Award just took hold of me."
Cutcliffe's No. 22 Blue Devils will play No. 20 Texas A&M in Tuesday night's Chick-fil-A Bowl. This is the first time Duke will play in back-to-back bowl games. Duke is playing for its first bowl win since 1961.
Kansas State's Bill Snyder won the 2012 award, named for the former longtime Georgia Tech coach.
Cutcliffe also has been named the Walter Camp and Maxwell Award coach of the year honors this year.
The Chick-fil-A Bowl is taking over management of the Bobby Dodd Award in 2014 and arranged a dinner for the former winners.
"We aim to make this similar to the Heisman Trophy for players," said Chick-fil-A Bowl president Gary Stokan. "We want this to be the Heisman Trophy for coaches."
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