Airport employees then paged Abuelazam over the intercom and, when he came to the desk, he was taken into custody without incident, an Atlanta Police Department report said.
Police believe Abuelazam may be behind 18 knife attacks beginning in May that spanned Michigan, Virginia and Ohio. Five of the victims died from their wounds -- David Motley, 31, Emmanuel A. Muhammad, 59, Darwin Marshall, 43, and Arnold R. Minor, 49, all of Flint, and Frank Kellybrew, 60, of Flint Township, Mich., according to The Associated Press.
The serial stabber was blamed for as many as 20 attacks at one point, but police determined two of the reported assaults were not likely linked to the serial stabber.
Most of the stabbing victims were black men, but Leyton declined to say the attacks were racially motivated.
"We don't have a motive yet but, as you know, many times the motive doesn't appear until later in the investigation," Leyton said Thursday. "Jury instructions don't require us necessarily to have a motive."
Leyton added that a police hotline on the case received more than 500 tips, including the one that sent police looking for Abuelazam.
Abuelazam, who was born in Israel and is of Arab descent, was living in the U.S. legally and has been linked to cities across the country.
Police believe he came to Michigan in May, just days before the attacks began.
Prior to the attacks, Auelazam had several run-ins with the law including several traffic violations, a check fraud charge and unlawful possession of a weapon. In 2008 he was arrested and held for obstruction of justice. He spent at least one month in jail for a fraud conviction in California.
Abuelazam's ex-wife, who lives in Texas, told The Detroit News she, too, was shocked by the arrest, but hadn't spoken to her ex-husband for a while.
Though the attacks took place from late May through early August, Leyton said law enforcement acted quickly.
"The first two crimes were homicides. The first one was in May and then about a month later was the second one. For those first two, we had absolutely no statement, no suspect, no evidence, no witness. So we had nothing right there," he said. "When we began to see the pattern emerge in late July, that's when everybody said 'This is what we have.'"
Leyton said Abuelazam could face charges in other states in addition to those in Michigan.
One of the victims, Richard Booker, 49, recently was released from a Flint hospital where he has been for the last three weeks after being stabbed. He told ABC News that he has 68 staples throughout his back and belly and has slash wounds on his arms because he tried to prevent the man from "cutting off his face."
"I've never hurt so much in my life, never come so close to death," Booker told ABCNews Wednesday. "I was about dead."
Booker, who is white, dismisses the notion that the attacks are racially motivated.
"I'm obviously not black. The guy's just a stone cold killer," Booker said.
Booker was stabbed five times, including a roughly 12-inch-long vertical slash from below his belly button all the way up his chest. He lost eight pints of blood from his wounds.
Antwoine Marshall, who was attacked two weeks ago, described a similar experience and similar wounds. He told ABC News he was stabbed six times in his stomach and chest.