The wide receiver's contract is worth $8.2 million and includes a $4.4 million signing bonus, a league source told ESPN NFL Insider Adam Schefter.
A wide receiver out of Baylor, Wright is expected to play a big role in Tennessee's offense.
Starting receiver Kenny Britt is on the physically unable to perform list with knee problems and also may be facing discipline from the league regarding a DUI arrest in Kentucky earlier this month.
At Baylor, Wright served as the primary target for Heisman Trophy winner Robert Griffin III, and was the 20th pick overall in the draft.
Information from The Associated Press was used in this report.