Prior to the announcement, the Penn State Board of Trustees' Committee on Compensation unanimously approved Barbour's employment terms.
Her 5-year contract has a base salary of $700,000, including $100,000 per year in retention bonuses and a maximum of $100,000 annually for meeting performance goals based on graduation rates, national championships won and postseason appearances.
Barron said Barbour was the first choice - "the clear choice" - of the screening committee, citing her 30 years serving in a leadership role at several institutions.
"We looked for a person who could continue providing experienced leadership . . . in addition to having proven skills at the highest level," Barron said. "I anticipate with her wealth of experience, that her entry into the Big Ten will be a smooth one."
Barbour replaces Dave Joyner, who had been in charge of Penn State athletics since November 2011. Joyner took over for Tim Curley, who was placed on administrative leave after allegedly covering up allegations in the Jerry Sandusky child-sex abuse case.
The school announced a month ago that Joyner would retire effective Aug. 1, but stay on until Aug. 17. Barron said Joyner will be a consultant, helping Barbour with the transition.
Joyner, who hired football coaches Bill O'Brien and successor James Franklin, had doubters and issues during his tenure. And Barbour enters the Nittany Lions fold with questions surrounding her time at Cal.
According to NCAA data released last fall, Cal football's graduation rate was the worst in the FBS. The basketball program also graduated less than 50 percent of its players.
Barron said he called Cal's current chancellor to discuss APR - Academic Progress Rate - and came away from the conversation under the impression that Barbour was a "champion" for the students and pressure the school to improve.
When asked about those figures, Barbour used one word: "Unacceptable."
"I learned some things from that situation that will benefit Penn State," said Barbour, adding that Penn State football's graduation rates will go from 85 to 90 percent. "Our student-athletes will be students first."
Franklin was among Penn State coaches attending the news conference in a show of support for Barbour.
Franklin, who said he briefly met with Barbour on Saturday morning, said he knows academic achievement is important to the entire administration.
"I'm just happy now that all the pieces of the puzzle are in place and we can continue moving forward, healing and growing," said Franklin, who did not have a hand in selecting Barbour. "I think the most important thing is that there's a history, culture and tradition of tremendous academic achievement and that will continue."
Outside of academics, Barbour, who oversaw 19 national team championships and 111 individual titles in her tenure at Cal, made it clear that success on the field will be held in high regard, as well.
"We aspire to national championships in each of our 31 sports," Barbour said. "National championships are the goal."
Barbour also recognized the challenges the Penn State community has faced in the past few years, saying that "family together can get through anything."
"Like any family, there have been remarkable highs and devastating lows," Barbour said. "Despite it all, Penn State remained glued together by a legacy of commitment to compete against all odds and to excel at the highest level."