The Bucs selected the All-American who helped the Crimson Tide win two national titles with the seventh pick of the NFL draft on Thursday night.
It's the third straight year the Bucs, who allowed a franchise-record 30.9 points per game while going 4-12 in 2011, have used their top pick in the draft on a defensive player.
"I think he fits into what we do defensively perfectly," Schiano said. "You watch him play ... you see the toughness, the leadership he brings to a football team."
Tampa Bay began the night with the fifth pick. But after Cleveland moved up one spot to No. 3 to ensure they'd get Alabama running back Trent Richardson, the Bucs traded down to No. 7 in a deal that also landed a fourth-round pick from Jacksonville.
Cornerback Morris Claiborne also was high of the Bucs' wish list. However, Dallas pulled off a deal with St. Louis to move up eight spots to No. 6 to take the former LSU star.
General manager Mark Dominik insisted the team targeted Barron for the fifth pick, but felt there was a good chance they could drop a couple of spots in the draft order and still be able to get the 6-foot-1, 213-pound Barron, who was an important component of a team that led the nation in rushing, passing and total defense last season.
Dominik said he never seriously considered trying to trade up, a move that may have given the Bucs a better shot at landing Richardson, who would have addressed the need for an every-down running back.
Dominik launched a youth movement that transformed the Bucs into the league's youngest team by selecting quarterback Josh Freeman in the first round in 2009. He focused largely on rebuilding the defense by using the team's first two picks in each of the past two drafts on defensive linemen.
The Bucs went 10-6 in 2010 and seemingly were headed into the right direction before collapsing following a 4-2 start last season. Morris was fired in January and replaced by Schiano, who spent the past 11 seasons turning one of college football worst programs into a consistent winner at Rutgers.
Barron will be plugged into a defense that ranked 30th among 32 teams in yards allowed.