The school is expected to announce the hire Friday, a source said. He would be the first significant hire by Troy Dannen, who became athletic director last week after holding the same post for almost eight years at Northern Iowa.
Fritz led the Eagles to an 8-4 record (6-2 Sun Belt) this season and a berth in the GoDaddy Bowl against Bowling Green.
The 55-year-old Fritz is 17-7 in two seasons with Georgia Southern, his first FBS coaching job. Georgia Southern went 8-0 in conference play last season to win the Sun Belt but was in transition from the FCS and therefore not bowl eligible.
He previously was the coach at Central Missouri (1997-2009) and Sam Houston State (2010-13) and took the Bearkats to back-to-back FCS title game appearances in 2011 and 2012.
Tulane fired coach Curtis Johnson last month after the Green Wave (3-9) finished their third losing season in four years under the New Orleans native.
Information from The Associated Press contributed to this report.