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Arrow replaces John Pelphrey, who was hired at Arkansas.
The job was "too tough to pass on," Arrow told the Corpus Christi-Caller Times for Tuesday's editions.
Arrow led TAMUCC to the NCAA tournament and a near-miss in the first round against No. 2 seed Wisconsin. Arrow started the Islanders' program from scratch and watched it develop from a D-1 startup to winning the Southland Conference.
South Alabama has been one of the top programs in the Sun Belt, and athletic director Joe Gottfried was looking for a coach who could continue the tradition of keeping USA in the heart of the title chase ever year.
Ironically, Arrow was once the coach at South Alabama, fired by a previous administration.
"The facilities and the league were big points," Arrow told the Caller-Times. "I've known [Gottfried] for such a long time. It's too tough to pass on."I'll always have my eyes toward this place down here. They allowed me the chance to start a program. This has been my baby, and I hope they have someone who can take it over and keep it going." Arrow went to the NCAA Tournament with USA in 1989 and '91. South Alabama beat Alabama in the first round of the 1989 NCAAs, losing to eventual champion Michigan in the second round. Arrow was the 1989 Sun Belt coach of the year.
TAMUCC finished 26-7, 14-2 in the Southland. South Alabama finished 20-12 overall, 13-5 in the Sun Belt.
Arrow got the job after Charlotte coach Bobby Lutz turned down an offer on Sunday.
Andy Katz is a senior writer at ESPN.com. Information from The Associated Press was used in this report.