Elton Simpson, 30, had linked himself to ISIS in a tweet posted just before the attack, a federal law enforcement source said.
Federal Agents were searching an apartment in Phoenix, Arizona, where Simpson reportedly lived, an FBI official said.
In 2011, he was convicted of making a false statement involving international and domestic terrorism.
He had previously been investigated on suspicion of terrorism offences.
The two gunmen were named on Monday as Elton Simpson and 34-year-old Nadir Soofi, who was a roommate of the former, The Washington Post reported, citing a law enforcement official.
Simpson had been under surveillance since 2006 and convicted in 2010 of lying to FBI agents over his desire to join violent jihad in Somalia, according to court documents.
FBI agents and police searched the two men's home at the Autumn Ridge Apartments in north-central Phoenix, cordoning off the complex and evacuating residents for several hours.
The controversial event was wrapping up shortly before 7 pm when the two gunmen pulled up in a car and shot an unarmed Garland ISD security officer.
Seconds later, Garland police returned fire and killed the two gunmen before anyone else was hurt.
One of the officers, a traffic policeman, returned fire and killed both the gunmen, said Garland police official Joe Harn.
"Obviously they were there to shoot people," Harn said.
The event featured speeches by Pamela Geller, president of the American Freedom Defense Initiative (AFDI), and Geert Wilders, a Dutch lawmaker known for his outspoken criticism of Islam.