The deal is worth $20.6 million, including a $13.3 million signing bonus and will be fully guaranteed, according to NFL.com's Ian Rapoport.
Bortles was the team's first pick, taken third overall in last month's draft after throwing for 3,581 yards and 25 touchdowns last season at Central Florida.
The team has two unsigned draft picks, receivers Marqise Lee and Allen Robinson, who were both taken in the second round.
“It’s awesome,” Bortles said, via the team's website. “It’s awesome to be able to kind of put this in the past. It’s a once in a lifetime thing, signing your first contract. It’s a cool feeling.”
Four first round picks still remain unsigned: Cleveland Browns cornerback Justin Gilbert, taken 8th overall, Tennessee Titans offensive tackle Taylor Lewan (11th), Miami Dolphins offensive tackle Ja’Wuan James (19th) and New England Patriots defensive tackle Dominique Easley (29th). MORE COVERAGE: Offseason Report Cards | NFL Power Rankings | 2015 NFL Mock Draft | Audibles podcast