The Titans agreed to send a 2022 second-round draft pick and a 2023 fourth-rounder to the Falcons in exchange for Jones. Atlanta also sent a 2023 sixth-round selection to the Titans in the deal.
The trade is pending a physical, according to the teams.
"Excited to add Julio to the football team. He's excited to be part of what we've got going on in Nashville," Titans general manager Jon Robinson told reporters Sunday. "It's a big day for our team."
Robinson said discussions gained steam Saturday before the two clubs agreed to terms Sunday.
Along with Jones passing a physical, Robinson said the Titans also will have to fit the wideout's large contract under their salary cap. The executive indicated that would likely happen through restructuring contracts and not releasing players.
"He's big, he's fast, he's tough, he's great with the ball in his hands, a willing blocker," Robinson said of Jones. "I think a lot of things that we ask of our receivers ... get open, catch and block -- he certainly checks those boxes and has done it at a high level in the National Football League."
The Titans lost two of their top pass-catchers earlier this off-season as wide receiver Corey Davis signed with the New York Jets and tight end Jonnu Smith joined the New England Patriots. Tennessee also lost slot receiver Adam Humphries, who signed with the Washington Football Team in March.
Jones was the subject of trade rumors over the past two months as the Falcons tried to fix their salary-cap woes. On FS1 in late May, Jones said, "I'm outta there," when asked about his status with the Falcons in a telephone call with Shannon Sharpe on the network's Undisputed show.
It remains unclear whether Jones was aware that the phone call was being televised.
The 32-year-old Jones, whose base salary of $15.3 million is fully guaranteed for this season, was set to cost the Falcons $23.05 million against the cap in 2021. According to Spotrac, he has cap hits of $19.3 million in 2022 and 2023.
The Falcons selected Jones with the No. 6 overall pick in the 2011 NFL Draft out of Alabama. He is the franchise's career leader in receptions (848) and receiving yards (12,896) and is second to Roddy White in touchdown catches (63).
"Julio Jones will always be a part of the Falcons story, having set numerous records and creating many great memories for all our fans, including me, since the day we drafted him," Falcons owner Arthur Blank said in a statement. "He has been a fixture on our team for almost half the time I have owned the Falcons.
"As we both move in another direction, I'm deeply grateful for what Julio has done for our team and what he has meant to our city and, in my mind, he will always be part of the Falcons family. I wish him nothing but the best in Tennessee and throughout his life."
Jones, a seven-time Pro Bowl selection, had one of his worst seasons in 2020. He was limited to just nine games because of injuries, recording only 51 catches for 771 yards and three touchdowns.
The Falcons have multiple options to replace Jones. Calvin Ridley, an All-Pro choice in 2020, will slide into the No. 1 role, and a combination of first-round pick Kyle Pitts, Russell Gage, Olamide Zaccheaus and sixth-rounder Frank Darby could see greater roles with Jones gone.