Woodyard will sign a four-year, $16 million deal, his agent told ESPN's Josina Anderson.
"Wesley is a player who has experience playing in both 3-4 and 4-3 systems, and in our new scheme he fits as one of the inside linebackers," Titans general manager Ruston Webster said. "He is smart and fast. He also brings the leadership qualities and intangibles that we look for in a player, which makes him a good fit for us."
Woodyard had been a team captain, either on special teams or defense, since he made his first roster as an undrafted rookie in Mike Shanahan's last season with the Broncos (2008), and in 2012 he was the only player in the league with at least 100 tackles, five sacks and three interceptions.
In 2013. he was moved to middle linebacker after Stewart Bradley suffered a season-ending injury during the team's preseason loss to Seattle. Woodyard, who is undersized for the middle and is more comfortable on the weak side, also suffered a stinger during the Broncos' regular-season win at Dallas and missed two games, and the coaches didn't think he was quite the same player after that.
The Broncos eventually moved Paris Lenon into the middle in the base defense, and Woodyard played in situational work. In all, he played 66.7 percent of the defensive snaps.
Information from ESPN.com Broncos reporter Jeff Legwold was used in this report.