Kelly, 43, took over the Georgetown football program in 2006 as his first head coaching position. He had one winning season -- 2011 when the Hoyas went 8-3 -- and was 24-63 overall.
Georgetown was 2-9 in 2013, snapping a seventh-game losing streak with a 28-21 season-ending win over Holy Cross.
Kelly is to be the defensive coordinator at Ball State.
"We are grateful to Coach Kelly for his service to Georgetown and for his devotion to the education and overall development of his players," Georgetown Athletic Director Lee Reed said.
"While on the Hilltop, he embraced the challenge of coaching this program in the highly competitive Patriot League and has helped to build a strong foundation. We wish him well in his new position."
The Hoyas said Rob Sgarlata, who was Georgetown's assistant head coach and defensive coordinator, was named interim coach as the school announced a national search for a full-time replacement for Kelly.
Georgetown is the only member of the Patriot League that doesn't offer football scholarships.