Fritz, who was 40-15 in four years with Sam Houston State, will succeed Jeff Monken, who was named Army's coach on Dec. 24.
Fritz, 53, led Sam Houston State to the Football Championship Subdivision championship game in 2011 and 2012, losing both years to North Dakota State. He moves to Georgia Southern, which has a rich tradition on the FCS level and now is moving up to the FBS as a new member of the Sun Belt Conference.
Georgia Southern won six FCS (formerly Division I-AA) national championships.
Fritz said he was attracted to Georgia Southern by "the opportunity to compete at the highest level and to be at the ground level" of the move to FBS.
"We want to continue the success at FCS at the highest level of college football," Fritz said. "I want to be involved in that type of situation."
Georgia Southern has achieved most of its success while running the triple-option, and Fritz said he will bring his version of that offense to Statesboro.
"We're a triple-option type team," Fritz said. "We do it a different way than you have been doing it here. ... We've rushed for a lot of yards. We're the leading scoring offense in FCS the last three seasons."
Georgia Southern president Brooks Keel said Fritz is a "perfect fit for this program."
Fritz has a 176-67-1 record in 21 years as a head coach. He was named coach of the year by the American Football Coaches Association in 2011, when Sam Houston State finished 14-1.
He previously coached at Central Missouri, where he was 97-47 in 13 seasons, and Blinn College.
"He's been able to win with other people's players and he's been able to recruit and win with his own players," said Georgia Southern athletic director Tom Kleinlein. "He's won at a lot of different levels and at a lot of different places. ... He will put his own stamp on this program and lead us into the Sun Belt Conference."
Georgia Southern finished 7-4 in 2013, including a shocking 26-20 win at Florida to close the season.
"This is my fourth head coaching job," Fritz said. "At the other three schools, the common denominator was the programs were on a downward spiral. That isn't the case here."
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