Jones believes Tennessee can recapture its past glory.
"Our fan base and myself have the same expectations," Jones said. "We're working to be the best. We're working to be No. 1 every day. We're working to be national champions, and we're working to be SEC champions. This program has done it, and we'll do it again."
Hart said at the start of the search that head coaching experience was "critically important" and that he wanted a coach who "knows the difficulty of climbing the ladder in the SEC." Jones lacks SEC experience, but his teams have earned at least a share of a conference title in four of his six seasons as a head coach.
"Les Miles and Nick Saban had zero SEC experience when they came into this league," Jones said.
After replacing Notre Dame coach Brian Kelly at Central Michigan and then again at Cincinnati, Jones maintained the momentum his predecessor had established at each school.
In Jones' three-year stint at Central Michigan, the Chippewas won two Mid-American Conference championships. Jones went 4-8 in his first year at Cincinnati, but the Bearcats are 19-6 since and have tied for first place in the Big East each of the last two seasons. Cincinnati's 2011 season included a 45-23 loss at Tennessee.
Jones, the third consecutive Cincinnati coach to leave after three years, signed a contract extension after the 2011 season that included a $1.4 million buyout if he left before Jan. 1. Mark Dantonio went 18-17 at Cincinnati from 2004-06 before Michigan State hired him away. Kelly posted a 34-6 record before leaving for Notre Dame.
Cincinnati has made defensive line coach Steve Stripling its interim head coach for the Dec. 27 Belk Bowl against Duke in Charlotte, N.C., while it begins searching for Jones' successor.
"Obviously we'd like to find somebody who would be committed here for a long time, and I think we're prepared to make those investments necessary to do that," Babcock said.
Now that he's left Cincinnati for Tennessee, Jones has plenty of challenges ahead.
He must restore a sense of order to a program that has lacked stability amid all these coaching changes. He also must win over a fan base that sought a bigger name and doesn't know much about him beyond the fact his Bearcats couldn't beat Dooley's Vols a year ago.
"You don't move backward," Hart said. "You move forward. I think that's what we have to do now as a fan base. Our alumni, our fan base, we've got to come back together as one. We've got to come back together and get Tennessee football back where we all want it."
Hart believes he's found the guy to get Tennessee there, even if he wasn't the Vols' first pick.
AP Sports Writers Joe Kay in Cincinnati, Larry Lage in Ann Arbor, Mich., and Teresa Walker in Nashville, contributed to this report.