Cutcliffe, a former offensive coordinator with the Vols, had talks with Tennessee on Thursday to potentially replace Lane Kiffin, who bolted the program on Tuesday to become USC coach.
"You follow your heart in big decisions," Cutcliffe told ESPN.com's Heather Dinich. "I have a lot of ties and a lot of people that I'm very close to, and a lot of respect for the University of Tennessee, but my heart is here. We've worked very hard these two years to change the culture, to change the team physically. You feel like the job's not done, and in this era, it bothers me, what we do as coaches, moving here and there. This is mid-January. Nothing about that felt right to me as a person."
Duke is 9-15 in two seasons under Cutcliffe after winning only 10 games in the previous eight seasons combined.
Duke athletic director Kevin White said Cutcliffe told him Friday morning that he "intends to remain the Duke football coach for a long time."
"Simply put, we could not be happier or more excited about the future of the Blue Devils football program," White said.
Cutcliffe's withdrawal from Tennessee's search follows that of Texas defensive coordinator Will Muschamp, the Longhorns' head coach-in-waiting, who turned down a lucrative offer from Tennessee, sources close to the situation told ESPN.com.
Tennessee athletic director Mike Hamilton continues to work toward having a coach in place by this weekend. The recruiting period goes live again on Sunday, and the Vols are working feverishly to have a new coach in place by then.
Kippy Brown, in his third stint at Tennessee, is the Vols' interim coach. Brown on Wednesday said he's been told that he also would be considered for the permanent head-coaching job.
Information from ACC blogger Heather Dinich and SEC blogger Chris Low was included in this report.