Gundy took to Twitter on Tuesday night to announce his intentions.
A former Cowboys quarterback, Gundy, 50, has spent 23 of his 28 years in coaching at Oklahoma State, the last 13 as head coach. Since 2010, he has led the Cowboys to at least 10 wins five times and guided them to an outright Big 12 title in 2011.
Oklahoma State is one of only seven schools to appear in every set of College Football Playoff rankings since 2015. The Cowboys (9-3) are No. 19 this week.
This is the second time Tennessee has made a run at Gundy. The Vols met with him prior to hiring Butch Jones in 2013, but Gundy also decided then to remain at his alma mater.
The Vols were prepared to make Gundy one of the highest-paid coaches in the SEC, sources said Tuesday.
Tennessee also has reached out to Purdue coach Jeff Brohm and Auburn defensive coordinator Kevin Steele about the job, according to multiple sources. The Vols are looking to replace Jones, who was fired Nov. 12.
Before Gundy called them to say he was returning, Oklahoma State officials feared his flirtation with Tennessee more seriously than they had the other jobs in the past, sources said.
Gundy's developing interest in Tennessee was heightened by another setback in his relationship with Oklahoma State athletic director Mike Holder, according to sources. Gundy had met with Holder and other Oklahoma State officials in recent days over a list of items Gundy believed would help recruiting efforts. Sources said talks between Holder and Gundy did not go well.
One sticking point has been Gundy's desire to put banners commemorating Oklahoma State's past bowl appearances in the indoor practice facility.
Gundy's relationship with Holder is being strained at a time when his relationship with mega-booster T. Boone Pickens has improved. Pickens, who has been critical in the past, issued a letter of support to Gundy following Oklahoma State's loss to rival Oklahoma earlier this season.
Gundy signed a five-year contract extension with Oklahoma State last summer.
Information from ESPN's Jake Trotter was used in this report.