Tad Cummins was arrested in northern California, the Tennessee Bureau of Investigation announced.
The pair, missing for a month, were found near the remote Shasta-Trinity National Forest, the Tennessean newspaper reported.
Mr Cummins had been seeking work in the area, according to the owner of the property where his car was discovered.
A lawyer for the girl's family said: "There aren't words in the English language to describe the level of relief and elation experienced by the Thomas family."
Jason Whatley added: "Now begins another hard chapter, but for now, we celebrate."
The girl has not yet spoken to her family due to her location being too remote, he said, and police officers were forced to trek through snow to capture him.
The 50-year-old had been Elizabeth's teacher at Culleoka Unit School in Maury County, Tennessee.
Tennessee officials said that he "may have been abusing his role as a teacher to groom this vulnerable young girl for some time in an effort to lure and potentially sexually exploit her".
The two disappeared on 13 March, weeks after a student reported seeing them kissing inside a classroom.
Shortly afterwards, they were spotted on surveillance cameras at a Walmart in Oklahoma City, but they had not been seen since.
Mr Cummins was suspended in February from teaching after failing to adhere to school administrators orders to stay away from the teenager.
Authorities say that before disappearing, Mr Cummins had carried out online research on "teen marriage".
He also purchased hair dye, took out a $4,500 (£3,600) personal loan, and researched if his Nissan Rogue vehicle could be tracked, officials say.
Police had considered Mr Cummins armed and dangerous during the manhunt.
According to a legal petition filed in court by the girl's family earlier this month, Mr Cummins is a "masterfully manipulating predator" who forced Elizabeth to go out with him by threatening her with repercussions at school.
According to the court papers, Mr Cummins - who had been married for 31 years - would visit the girl at home to pick her up for meals, as well as come to the fast food restaurant where she worked.
"The child had told various siblings and/or friends that she was scared of Cummins and felt in over her head," the documents show.
Jill Cummins, the suspect's wife, filed for divorce as officials closed in on her husband.
"It's very selfish of him to have done this to us," she told ABC News.
"I do love him, but I don't trust him anymore. He's totally betrayed me," she went on to say.
Authorities had chased more than 1,500 leads in all 50 states, according to Tennessee Bureau of Investigations Director Mark Gwyn.