Shomper has been on paid administrative leave since Feb. 12 when search warrants were executed at his Tippecanoe High School office, his home and his vehicle.
The searches were part of an investigation initiated in September when Superintendent Gretta Kumpf reported to Tipp City police irregularities found by state auditors in the athletic department.
The investigation continues and no charges have been filed.
Shomper signed the separation agreement Monday, but has seven days to revoke the agreement, said attorney David Lampe, who met with the board in a closed-door session before the vote.
Kumpf recommended the board approve the agreement and resignation to “avoid the time, cost and uncertainty of pursuing other measures.”
Shomper has been the athletic director since 2006. The district last week hired an interim high school athletic director, James Smerz of Centerville. The board said Monday it would work to select a permanent director for the 2016-17 school year.
The board declined further comment, saying it is its practice “to not publicly comment about matters affecting specific personnel.”