Hayes, an Atlanta native and University of Georgia alumnus, replaces Rob Lanier, who left Georgia State to head SMU's program.
Hayes, 40, was an assistant coach at Xavier before being promoted to interim coach after Travis Steele was fired following a win over Cleveland State in the first round of the NIT.
Hayes then led Xavier to its first NIT title since 1958 with wins over Florida, Vanderbilt and St. Bonaventure before a 73-72 victory over Texas A&M in Thursday night's championship game.
Georgia State athletic director Charlie Cobb said Hayes was the school's choice after interviews with multiple candidates.
"Jonas is an experienced leader who will build a staff that embraces our expectation of competitive success, develops men of character and engages our community positively and with energy," Cobb said.
Lanier was 53-30 in three seasons at Georgia State and took the Panthers to this year's NCAA tournament. It was Georgia State's fourth NCAA appearance in eight years. Former Arizona coach Sean Miller was hired for his second stint at Xavier.
Hayes spent four years at Xavier after six seasons as an assistant at Georgia.
Hayes began his coaching career as an assistant coach at Atlanta's Morehouse College in 2005. He launched his collegiate playing career at Western Carolina before transferring with his twin brother, Jarvis, to Georgia, where he played from 2001 to 2004.