Kelsey Peterson, a 25-year-old sixth-grade math teacher and basketball coach at Lexington Middle School, was arrested in Mexicali, a city on the border with California, Dawson County Attorney Elizabeth Waterman said.
They were found and apprehended by Mexican authorities without incident Friday evening. Peterson was in FBI custody and transported back to the U.S. early Saturday, and the boy was released to relatives in Mexico, Waterman said.
"I'm really relieved, especially that the individuals are well and unharmed," Waterman said.
Peterson and the boy fled after police began investigating whether the pair had an intimate relationship, authorities said. Court documents said the boy was last seen Oct. 26.
Waterman said she did not have details on how the pair were found or where Peterson was being held. She said FBI agents were holding her on federal charges.
Calls to FBI and U.S. attorney officials in Omaha were not immediately returned Saturday.
A judge issued an arrest warrant Monday charging Peterson with kidnapping, child abuse and contributing to the delinquency of a minor.
Peterson also faces federal charges, including transporting a minor across state lines or a foreign border for sexual activity, U.S. Attorney Joe Stecher said. Those charges were filed Thursday.
The boy, Fernando Rodriguez, was an eighth-grader at the school, but district Superintendent Todd Chessmore said Rodriguez had been in Peterson's 6th-grade math class.
The Associated Press generally does not identify people who may be victims of sex crimes, but the boy's name had been widely publicized as police searched for him.
Fernando's aunt, Laura Rodriguez, said Saturday that the boy was likely with an uncle in Mexicali. She said family in California and Mexico had already been searching for him.
Rodriguez said the family had not been told by any officials that Fernando had been found.
Peterson's car crossed into Mexico on Tuesday at the San Ysidro Port of Entry, which separates San Diego and Tijuana, Mexico, Lexington police said. The car's license plate was captured by an automated system that scans the plates of all vehicles passing through the entry point.
Cars typically are not stopped on the way out because "our focus is on what's entering the United States," said Vince Bond, a spokesman with U.S. Customs and Border Protection in San Diego.
Court documents showed authorities had recovered several e-mails and letters in which Peterson and the boy professed their affection for one another.
In letters, the boy called Peterson his "Baby Gurl" and said their relationship was "just not about the sex but that it was pretty good," according to the court documents.
Peterson's school-issued laptop contained letters to the student, including one from April saying she loved him, thought he loved her, was "100 percent faithful" to him and would always be faithful, the court documents state.
Laura Rodriguez also said the family believed Peterson gave the boy a cell phone without his family's knowledge so she could reach him more easily. Messages left on a cell phone for a Kelsey Peterson of Lexington were not returned.
Lexington Schools Superintendent Todd Chessmore said he placed Peterson on paid administrative leave on Oct. 25.