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.
Then in a surprise move, they later completed a trade that netted a second first-round pick and used it on Boise State running back Doug Martin.
"As a rookie, I want to come in and establish myself as one of the best players in the league, and hopefully win the rookie of the year award," Barron said by telephone from New York, where he described himself as excited and "really surprised" to be picked that early in the opening round.
"It's a great opportunity for me to go down and prove I'm worth that seventh pick," he added. "I feel I can go in and do whatever I need to do for this team."
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 on a defensive player. It's the first time in team history that Tampa Bay has used a No. 1 on a safety.
First-year coach Greg Schiano said the 6-foot-1, 213-pound Barron, was a dominating player in college football's most competitive league and has a chance to be an elite player on the next level as well.
"This guy has got the ability to do some special things," Schiano said, adding that Barron is a perfect fit for what the Bucs want to do defensively. "It's going to be a long process. We're going to work very hard it. But he has got what it takes, I believe in all areas, to be really special."
Schiano was just as excited about landing Martin, who averaged 5.56 yards while rushing for 3,431 yards and 43 touchdowns in four college seasons.
"I feel like we're in a position where we got two great football players. ... Young men who are going to come in here and have an impact add energy to this organization," the coach said.
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, general manager Mark Dominik traded down to No. 7 in a deal that also landed a fourth-round pick from Jacksonville, No. 101 overall.
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.
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 two-time Alabama captain, 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
To get Martin, the second running back selected Thursday night. the Bucs moved up six spots from the second round in a trade that sent the 36th overall pick to Denver. The teams also swapped fourth-round picks.
With Tampa Bay, the 5-9, 220-pound Martin will team with 240-pound LeGarrette Blount to give the Bucs what Schiano hopes will be a punishing ground game after ranking 30th in rushing offense a year ago.
Meanwhile, the selection of Barron comes less than a month after the Bucs released starting safety Tanard Jackson. It will be a disappointment it he isn't a starter from day one on a defense that ranked 30th among 32 teams in yards allowed last season.
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.