Prosecutors charged the men Friday with conspiring to provide material support to the organization.
The case filed in U.S. District Court in Santa Ana names Nader Elhuzayel and Muhanad Badawi, both 24.
Elhuzayel's parents were dropping him off at the Los Angeles International Airport for a flight to Pakistan when officials confronted the family, CBS Los Angeles reported.
"We find the FBI blocking us down the street and said we cannot enter the place," Elhuzayel's mother told CBS Los Angeles.
His parents then returned to their room at the Crystal Inn in Anaheim, where they were staying, to find a hole in their door and FBI agents in their room.
"We just come back and from nowhere the FBI raid our room. They broke our door. They made holes in there, they threw all our clothes and everything outside in the street," she said.
FBI officials also arrested Badawi at an Anaheim gas station. His apartment on South Street was also searched.
"They took computers and a bunch of stuff out of the house. There was a ton of cops out here and they blocked everything off. It was kind of scary," one resident said.
According to the affidavit filed in United States District Court filed in Santa Ana (PDF), Elhuzayel saw a tweet on May 3 from Elton Simpson, one of the two gunmen who were killed trying to attack a conference in Garland, Texas. Simpson's tweet pledged allegiance to the leader of ISIS, and Elhuzayel allegedly replied to the tweet by saying he supported the attempted attack and praised Simpson as a "martyr."
In recorded conversations last month, federal prosecutors say Badawi and Elhuzayel "discussed how it would be a blessing to fight for the cause of Allah, and to die in the battlefield," and they referred to ISIS as "we." According to the affidavit, the two men also discussed local Muslim leaders and Elhuzayel complained that these leaders were not "legitimate" because they believed in democracy and were not fighting for ISIS.
"We are Americans. We voted all our lives. We maintained good citizenship all our lives and all of a sudden they're trying to build a case," Elhuzayel's father said.
When asked if her son was involved with terrorists groups, Elhuzayel's mother responded:
"No one whatsoever," she said. "My son is a good kid."
The affidavit says Badawi allowed Elhuzayel to use his credit card on May 7 to buy a one-way ticket from Los Angeles to Tel Aviv, Israel, via Istanbul, Turkey, on a Turkish Airlines flight scheduled to depart on May 21, and that Badawi indicated he would travel to the Middle East at a later date.
According to the criminal complaint, after being read his Miranda rights, Elhuzayel admitted that he planned to disembark in Istanbul to join ISIL and did not intend to travel on to Israel.
The arrests involved the FBI, Anaheim Police Department and the Orange County Sheriff's Department.
Both are to appear in court Friday afternoon.