Rams head coach Sean McVay could have blocked the move but decided to let LaFleur, 38, advance in his career. The Rams promoted Aaron Kromer to run coordinator and Shane Waldron to pass coordinator after LaFleur's departure.
"I'm excited for Matt LaFleur and his family as he transitions to the Titans as offensive coordinator," McVay said in a statement. "We're grateful for his contribution to the Rams and our NFC West Championship season last year. As we move to 2018, we are confident in the leadership and guidance of Aaron Kromer and Shane Waldron as they begin their roles as run coordinator and pass coordinator."
The Titans also officially announced the hire of briefly retired Dean Pees, 68, as defensive coordinator. Pees spent the past eight seasons with the Ravens, including six as defensive coordinator before retiring on Jan. 1.
"I am excited to add both of these guys to our team," Titans head coach Mike Vrabel said in a statement. "Dean brings a great deal of experience and knowledge to our staff. I have seen first-hand how he teaches and develops from our time together and I wanted to bring that same experience to our players here."
Getting the most from Mariota and a talented Titans roster will be a priority for LaFleur. Tennessee advanced to the divisional round of the playoffs this past season, but Mariota took a big step back, throwing a career-low 13 passing touchdowns and a career-high 15 interceptions.
Titans general manager Jon Robinson stressed the importance of the relationship among Mariota, LaFleur, quarterbacks coach Pat O'Hara and Vrabel.
"Matt brings an energy and an offensive diversity to our team," Vrabel said in the statement. "He is going to develop an offense that puts our players in position to have success. Matt has worked with some great offensive minds, helped game plan on those staffs and I am looking forward to seeing him take that next step as a play-caller."
LaFleur's work with Goff in L.A. and Matt Ryan in Atlanta makes him an exciting candidate to work with Mariota in Tennessee.
LaFleur also helped ignite a Rams offense that went from last in scoring in 2016 to first in 2017. He was the Falcons' quarterbacks coach during Ryan's MVP 2016 season.
The Titans finished 23rd in total offense and 19th in scoring offense under Mike Mularkey's often-predictable "exotic smashmouth" offense. Terry Robiskie was the playcalling offensive coordinator last season.
Vrabel went with a mix of experience and youthful energy in filling his coordinator positions.
The Titans are expected to run more collegiate-spread scheme to maximize Mariota's ability in 2018. The Rams had success with the spread this past season, too.