Authorities said Charles McCoy, 28, was taken into custody without incident at the Budget Suites motel near the Stardust casino, and had not charged.
Police were told of McCoy's whereabouts by a person who recognized him from media reports linking him to the Ohio shootings, Las Vegas police Lt. Christopher Van Cleef said.
"He wasn't armed, but we haven't been in the motel room or his vehicle yet," Van Cleef said. He said police have impounded a 1999 Geo Metro that McCoy was driving.
FBI special agent Todd Palmer said McCoy is being processed in the agency's office and likely will be transferred to the U.S. attorney's office.
"They'll be in communication with the Columbus U.S. attorney," Palmer said.
The 24 shootings around several highways on the southern outskirts of Columbus pierced homes and a school, dented school buses, flattened tires and shattered windshields. They began in May.
Until January, the gunfire was scattered along or near Interstate 270, the busy highway that encircles Columbus. The last four shootings had moved toward the southwest on I-71.
The only person struck, Gail Knisley, 62, was killed as a friend drove her to a doctor's appointment Nov. 25.
Police issued a bulleting describing McCoy two days ago.
Conrad Malsom, 60, of Las Vegas said he told authorities he met McCoy at the Stardust casino Tuesday. He said he offered McCoy a slice of pizza but recognized the disheveled-looking man with a darkening beard.
McCoy was reading a copy of USA Today that featured his photograph, Malsom said.
"In my heart and mind, I knew this was the man the police in Ohio were looking for," Malsom said.
He said McCoy told him his name was "Mike" and that he was staying at the nearby motel. When he left the casino, Malsom found "bizarre writing" on an 8½ by 14-inch sports betting sheet the man left behind.
"It filled the whole sheet — about 30 lines," Malsom said. "Each line started with 'You' or 'You are' but you can't read it, you can't read any of it."
The shootings prompted commuters to take detours and schools to cancel classes or hold recess indoors. Police increased patrols and the state installed cameras on poles along Interstate 270.
From the beginning, investigators believed the shooter was familiar with the area around I-270.
In the three most recent shootings, witnesses described seeing someone aiming at them while standing next to a car. Their descriptions of the suspect and car were similar to information the sheriff's office released Monday.
Authorities haven't said what evidence led them to McCoy.
Bruce Cadwallader, a crime reporter for the Columbus Dispatch told the Early Show that McCoy's father, who had kept the guns, turned over two nine millimeter pistols. One of those turned out to be the murder weapon used to kill Knisley and has been matched to eight other bullets in this series.
An arrest warrant accuses McCoy of felonious assault in a shooting with a 9 mm handgun that damaged a house Dec. 15.
McCoy's sister Amy Walton, who had pleaded Tuesday for Charles McCoy to give himself up, told the CBS News Early Show on Wednesday that she was "extremely relieved" that the manhunt was over and that "no policemen were harmed. No ordinary citizens were harmed. And Charles is safe in custody right now. "
"This is certainly not the Charles that we knew," said brother-in-law Tye Walton. "We never saw him as an aggressive individual, never violent in any way."
Police have not suggested a motive for the sniper attacks, and few details have emerged about their suspect.
McCoy had reportedly been under psychological care, but had not been taking his medicine, reports CBS News Correspondent Randall Pinkston. Former FBI profiler Clint Van Zant told WBZ Radio in Boston that McCoy's behavior was a departure from what some mentally ill suspects might do.
"In some cases, if an individual is a paranoid schizophrenic, they would have a hard time leaving an area that they're comfortable in," Van Zant said. "But then again his common sense would tell him if he stayed in the same vehicle — his face, everything else — that he was so well known in the Ohio area that his choices would have been extremely limited."
"In this particular case it looks like he got in his vehicle and just fled thinking 'I'll go as far as I can, I'll go to a large population area where maybe I can blend in,'" Van Zant said.
In a missing person's report filed Monday, McCoy's mother, Ardith, said her son withdrew $600 from a bank account and left home Friday for a mall restaurant and bar with video games.
Neighbors on McCoy's street said they didn't know much about the suspect or his mother. A check of court records in nearby counties turned up a handful of traffic tickets for McCoy, but no other criminal or civil charges.
The tan garage doors at the house were splattered with three eggs Tuesday. Police said they did not know who hurled the eggs or when they were thrown.
McCoy's high school football coach said he's praying for his former player.
"He was an ornery kid, but a lot of kids are ornery at that age," said Brian Cross, who coached McCoy for four years at Grove City High School. "I don't remember him doing anything extreme."