The news of Barron's expected appointment was first reported by Onward State, a student-run blog at Penn State.
As Penn State's new leader, Barron will step into one of the highest-profile university presidencies in the nation. He will take over a campus still smarting from the fallout of the Jerry Sandusky sexual-assault scandal. And he will have to deal with a board still divided over the handling of the matter and with angry alumni.
The new president will be in charge of a 44,000-employee enterprise that has an annual budget of more than $4 billion and has coped with flat or declining state funding in recent years.
Trustees, Penn State officials, and Barron's office in Florida did not return calls for comment.
Barron's selection brought immediate praise from the Penn Staters for Responsible Stewardship, an alumni group that has been highly critical of the trustees' handling of the Sandusky scandal.
"It's encouraging to see the selection of an individual with ties to Penn State and an obvious appreciation of the exceptional culture that has been a hallmark of our university for decades upon decades," said Maribeth Roman Schmidt, a spokeswoman for the group. "Given Dr. Barron's climatology background, perhaps there is no one better suited to take the temperature of the alumni and the greater Penn State community in an effort to promote truth, transparency, and, ultimately, healing."
Barron will replace Rodney Erickson, who has led the 96,000-student, 24-campus university since Graham B. Spanier was forced out in November 2011, after word surfaced that Sandusky, a former assistant under legendary football coach Joe Paterno, had sexually assaulted boys, some of them on campus.
After he took the job, Erickson, 67, made it clear he wanted to leave by June 30 of this year.
Barron's appointment at age 62 raises speculation about how long he might remain - whether Penn State was seeking a leader to get it through the next few years while effects of the scandal linger. Spanier was president for 16 years.
The University of Pittsburgh last week chose Patrick D. Gallagher, who is 12 years younger than Barron, as its new chancellor.
Florida State is a sprawling system with about 41,500 students, encompassing 16 colleges that offer more than 275 undergraduate, graduate, doctoral, professional, and specialist degree programs, including medicine and law.
Under Barron's leadership, the university was ranked by U.S. News and World Report in December as the most efficiently operated university in the nation. And its football team won the national championship last month.
Barron earned a bachelor's degree in geology from Florida State in 1973 and his master's and doctoral degrees in oceanography from the University of Miami.
Before Florida State, he was director of the National Center for Atmospheric Research in Boulder, Colo., and dean of the Jackson School of Geosciences at the University of Texas at Austin. At Penn State, he was a professor of geosciences, and also served as director of the Earth System Science Center and director of the EMS Environmental Institute.
A native of Lafayette, Ind., he and his wife, Molly, have two children and one grandchild.
Barron becomes the second Florida education leader to take the helm of a major university system in Pennsylvania this year. Frank T. Brogan, who became chancellor of Pennsylvania's 14 state universities in October, hails from the State University System of Florida.
Florida State also has a distinct rivalry with Penn State.
For years, Paterno and Florida State football coach Bobby Bowden vied for to be the winningest coach in major-college football history. Bowden came out on top after the NCAA stripped Paterno of 111 wins in the Sandusky scandal.