BRADENTON, Fla. — A Mexican national surrendered at America’s southern border yesterday after allegations of abducting a 13-year-old from a Florida bus stop last month and leaving him tied up in the woods before the boy escaped, officials said.

Vicente Ignacio Beltran-Moreno, 22, agreed to voluntarily return from Mexico after several days of negotiations with the FBI, Manatee County Sheriff Charlie Wells said.

Mr. Beltran-Moreno was arrested yesterday morning at the America-Mexico border in Texas, and extradition proceedings were under way to get him back to Florida.

They convinced him he would be better off in an American prison, close to his girlfriend and two children, than incarcerated in Mexico, she said.

Clay Moore was grabbed February 23 while waiting at his school bus stop in Parrish. The gunman drove off with him in a red pickup truck, then left him tied up in the woods about 20 miles away.

The boy’s parents have said he freed himself by using a safety pin to pick apart the duct tape that held his wrists.

Mr. Beltran-Moreno became a suspect after investigators took an artist’s sketch to migrant worker camps east of Bradenton.

Investigators have said they believe that Clay was picked out at random and that the kidnapper planned to leave him tied up in the woods until a ransom was paid.

Clay was in school taking a standardized test yesterday. His stepfather, Steve Kelle, said the boy’s family was pleased with the arrest.

“We’re just overjoyed, and we’re glad we can get past this,” he said.