The fully-guaranteed contract is for four years and worth roughly $11.5 million, with a $6.7 million signing bonus, reports The Tennessean.
Lewan, an offensive tackle out of Michigan, was the last of the NFL's unsigned first-round draft picks.
With the Wolverines, Lewan was a two-time Big Ten offensive lineman of the year and an AP First-Team All-American.
Lewan faces a trial in October for assault and battery after allegedly punching an Ohio State fan after the Michigan-Ohio State game last November.
Titans players report to training camp on Friday.
- Molly Geary