The defensive end tweeted Saturday night that he was in a break room in the team's headquarters waiting to sign. Terms were not immediately available, but a league source told ESPN NFL Insider Adam Schefter the deal is for five years.
"And this is what they got on the table knowin I got to weigh in 2moro," Morgan wrote, tweeting a picture of boxes of Krispy Kreme donuts.
The Titans confirmed they agreed to terms with Morgan.
They used the 16th pick overall on Morgan hoping to boost the pass rush on a defense that ranked next to last in the NFL in 2009. He had 12½ sacks as a junior when he was first-team All-American and the Atlantic Coast Conference's defensive player of the year.
The Titans started training camp with six players on the physically unable to perform list, including starting defensive tackle Tony Brown and their third-round draft pick.
Brown had surgery to fix a problem in his knee and spent the offseason rehabing. Receiver Damian Williams hurt a hamstring in the 13th of the team's 14 on-field training sessions, and coach Jeff Fisher had worried about his condition. The Titans checked him out Saturday morning and found the third-round pick from Southern California isn't ready to practice yet.
Receiver Justin Gage needed fluids intravenously after practice, but not because of a heat index that reached 100 degrees. He has had an intestinal problem and left practice early. ... CB Tye Hill, one of four competing to start opposite Cortland Finnegan, had ice on the back of his right leg. He missed his turn at the rotation during the organized team sessions when he hurt a hamstring. ... DE Jason Jones practiced with the team for the first time since having shoulder surgery last December.
The Associated Press contributed to this story.