The shooting left at least 26 people dead and 20 others injured in what Texas Gov. Greg Abbott described as the worst mass shooting in his state's history.
Kelley is a former U.S. Air Force member who served from 2010 to 2014. Records confirm Kelley previously served in logistics readiness in New Mexico until his discharge in 2014, Air Force spokesperson Ann Stefanek said in a statement.
Kelley was court-martialed in 2012 for two counts of assault on his spouse and assault on their child, Stefanek said. He received a bad conduct discharge and confinement for 12 months.
He has a residence in New Braunfels, Texas, which is about a 35 mile drive from where the attack took place in Sutherland Springs.
Officials say the suspect lived in a San Antonio suburb and doesn't appear to be linked to any organized terrorist groups. CBS News has learned Kelley has a wife named Danielle Lee Shields.
Investigators will look at his social media posts made in the days prior to Sunday's attack -- including one that appeared to display an AR-15 semiautomatic weapon. Kelley's date of birth is listed as Feb. 21, 1991.
No motive has been declared as the investigation continues.
Sutherland Springs is about 35 miles southeast of San Antonio.
More about: #TexasChurchMassacre