With the move, Henry is officially under contract for the 2020 season. Both sides have until July 15 to negotiate a long-term contract to replace the franchise tag. If no agreement is reached before that deadline passes, Henry would have to play the 2020 campaign under the one-year tag.
On Wednesday, Titans general manager Jon Robinson told the team's official website there is mutual interest between the franchise and Henry on working out a long-term deal.
"I think any time a player, when you have to use the tag on them, that's something that ideally they probably don't want," Robinson said. "But still, at the same time, I know that he wants to be a part of this football team and I thought it was good that they communicated back he does want to be here, and does want to keep working on this thing.
"It wasn't something like, 'OK, well, I'll take the [tag] and I'm done, or I am just going to do whatever.' He wants to be here, and he conveyed the message to me, through his agent, that he wants to keep working on this thing and we do, too."
Henry, who turned 26 in January, won the NFL rushing title last season after compiling 1,540 yards on the ground. He has posted back-to-back seasons of more than 1,000 rushing yards.
The former Alabama Crimson Tide star, who was selected to his first Pro Bowl in 2019, averaged 5.1 yards per carry last season, leading all running backs with at least 200 carries.
Henry became the first tailback to receive the franchise tag after leading the league in rushing yards in the previous season.