The deal is for three seasons and $10 million, league sources told ESPN.
The Jets didn't see Greene as a fit in their new West Coast system and didn't make a strong push to re-sign him. The Titans targeted him because of his bruising running style, which they believe will be an ideal complement to that of Chris Johnson, which general manager Ruston Webster mentioned in the team's statement announcing the signing.
"He is a nice complement to Chris and an accomplished back in his own right," Webster said. "He is a tough and physical runner who has rushed for 1,000 yards each of the last two years."
The Jets' defense also took a hit Wednesday, with safety Yeremiah Bell signing with the Arizona Cardinals. Contract terms weren't immediately available. Bell started every game for the Jets last season and finished third on the team in tackles.
The Indianapolis Colts also announced that they have signed free agent safety LaRon Landry. With Landry gone, the Jets will have two new safeties for the second straight year, and there could be as many as nine new starters on defense.
Greene rushed for 1,054 and 1,063 yards, respectively, the past two seasons, but never developed into a legitimate No. 1 back. Even though he led the team with eight touchdowns in 2012 -- impressive on a team that finished 28th in scoring offense -- he wasn't a breakaway threat.
His departure leaves the Jets with no accomplished running backs, a dramatic drop-off. Unless they import a proven veteran, this will mark the first time since 1994 they don't have a 1,000-yard rusher on the roster.
Now they're left with Bilal Powell and Joe McKnight, who have a combined total of 960 yards. They almost certainly will draft a back, and they're interested in free agent Mike Goodson, most recently a backup with the Oakland Raiders.
"We do have a couple of fellas on our roster right now that have displayed some dynamic ability and the ability to catch the football," new offensive coordinator Marty Mornhinweg said this week, alluding to Powell, McKnight and former undraftred free agent John Griffin.
Greene made a huge splash as a rookie in 2009, emerging as a late-season force on a team that reached the first of two AFC Championship Games. He ran for 263 yards in his first two postseason games, the most by a rookie since 1970.
He shared the running duties with Tomlinson in 2010 and 2011, emerging as the No. 1 last season.
Greene, a former third-round pick, has 3,423 yards, a 4.2 average and 18 touchdowns in his career.
The Titans also reached an agreement with defensive tackle Sammie Lee Hill. According to league sources, Hill's deal is worth $11.4 million, including $4 million guaranteed.
Hill, who spent his first four seasons with the Lions, has registered 95 tackles and four sacks in his career.
"He is a big, athletic inside player. He should help us in the run game and he gives us a different body type," Titans general manager Ruston Webster said. "I see him fitting in well with our current group of tackles, which will have a quality rotation of players."
ESPN NFL Insider Adam Schefter contributed to this report.