According to ESPN's Adam Schefter, Tennessee previously interviewed LaFleur for its head coaching job.
The Titans hired Mike Vrabel as their head coach after parting ways with Mike Mularkey.
Vrabel said the following about the hires, per Jim Wyatt of the Titans' official website:
"I am excited to add both of these guys to our staff. Dean brings a great deal of experience and knowledge to our staff. I have seen firsthand how he teaches and develops from our time together, and I wanted to bring that same experience to our players here.
"Matt brings an energy and an offensive diversity to our team. 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."
After ranking last in points scored in 2016 (14.0 per game), the Rams led the NFL at 29.9 points per game in 2017.
Although head coach Sean McVay called the offensive plays, LaFleur's history of helping pro quarterbacks may have played a big role in Jared Goff becoming a Pro Bowler during his second season.
LaFleur was the Atlanta Falcons' quarterbacks coach in 2016 when Matt Ryan was named NFL MVP, and he helped mentor both Robert Griffin III and Kirk Cousins as the Washington Redskins' quarterbacks coach previously.
Pees' relationship with Vrabel likely had plenty to do with his decision since he was part of the New England Patriots' coaching staff from 2004 through 2009.
Vrabel played for the Patriots from 2001 through 2008, and Pees served as both his position coach and the defensive coordinator at various points during that tenure.
Pees is a two-time Super Bowl champion as an assistant, and he brings a wealth of experience to Vrabel's staff. The 42-year-old Vrabel is a first-time head coach, and he has just one season as a defensive coordinator under his belt.
In 2017, the Titans finished 9-7 and reached the playoffs for the first time since 2008. They also beat the Kansas City Chiefs in the AFC Wild Card Round before falling to the Patriots in the AFC Divisional Round.
LaFleur will work with quarterback Marcus Mariota and attempt to improve the NFL's No. 19 scoring offense, while Pees will inherit the league's No. 17 scoring defense.