The trade cannot be processed until the new league year begins March 18.
Bouye told ESPN's Josina Anderson that he was informed of the pending trade from both Jaguars general manager Dave Caldwell and Broncos president/general manager John Elway.
"I'm on the way to get my kids, [and] I get a phone call from Caldwell, saying he appreciates everything I did for the team," Bouye told ESPN. "Then Elway calls me, saying, 'Welcome to Denver.' Now everyone is calling. I'm just finding out. I want to thank Jacksonville."
Bouye was one of the key members of a 2017 free-agent class for the Jaguars that was regarded as the one of the best in franchise history. He is due to make $13 million and count $15.5 million against the salary cap in 2020.
Broncos cornerback Chris Harris Jr., a four-time Pro Bowl selection who has been with the team since being signed as an undrafted rookie in 2011, is set to become an unrestricted free agent.
"I'm definitely excited because Chris Harris always had good things to say about Denver," Bouye told ESPN. "I'm about to watch film and look at their scheme some more and really study it. It's cornerback-friendly. The three times I played there, the atmosphere and fan base was amazing."
Harris congratulated Bouye on Twitter:
Bouye had eight interceptions and broke up 34 others in three seasons with the Jaguars. His best season was 2017, when he intercepted six passes and broke up 18 as part of one of the league's best defenses.
Bouye, who turns 29 in August, made the Pro Bowl and was a second-team All Pro that season, but he did not consistently play at a high level the past two seasons.
He signed with the Houston Texans as an undrafted free agent in 2013. He took advantage of injuries in the secondary, starting 11 games in 2016 (one interception, 16 pass breakups) and cashed in with the Jaguars on a five-year, $67.5 million contract with $26 million guaranteed.
With Bouye gone, there are only four starters or key reserves remaining from the 2017 Jaguars defense that led the NFL in pass defense and finished second in sacks, interceptions and turnovers: defensive end Calais Campbell, defensive end Yannick Ngakoue, linebacker Myles Jack and defensive tackle Abry Jones.
Sources told ESPN on Monday that the Jaguars will use their franchise tag on Ngakoue.
Last week at the NFL scouting combine, Elway said the Broncos were going to make cornerback a priority in both free agency and the draft.
"I think we have to get better there," Elway said. "That's one area we're looking to get better."
The Broncos signed cornerback Bryce Callahan to a three-year, $21 million deal last offseason. Callahan, who was coming off December 2018 surgery to repair a foot fracture, did not play a snap in 2019 after having a second surgery to replace a surgically implanted screw, which he bent during training camp. He finished the season on injured reserve.
Broncos coach Vic Fangio expressed optimism during the combine that "all the reports I'm getting, including from Bryce, is that he'll be ready to go for camp."
ESPN's Michael DiRocco and Jeff Legwold contributed to this report.