Contract terms were not immediately available.
Smith led the Ravens in tackles in 2015, but the 33-year-old linebacker showed signs of slowing down toward the end of the season, when he split playing time with Zachary Orr.
"We're excited to add a player of Daryl's caliber to our defense," Bucs general manager Jason Licht said in a statement. "He's a smart, consistent linebacker who has performed at a very high level throughout his career. Daryl's combination of leadership and experience will serve us well."
He was released by the Ravens on March 3 with two years remaining on his contract. He was scheduled to earn $3.5 million in 2016.
Smith made over 120 tackles in each of his three seasons in Baltimore, helping the team make a smooth transition after the retirement of Ray Lewis.
Said Ravens coach John Harbaugh last season: "Daryl Smith is the most underrated linebacker in football, without question. I'll stand on that all day long."
Prior to joining the Ravens, Smith spent nine seasons with the Jacksonville Jaguars after being selected in the second round of the 2004 draft. He has 1,051 career tackles, 13 forced fumbles and 11 interceptions.
ESPN Ravens reporter Jamison Hensley contributed to this report.