A man has been charged with murder in connection with the disappearance of missing Iowa college student Mollie Tibbetts, police say.
Cristhian Bahena Rivera, 24, is in the US illegally, authorities say.
Remains believed to be Ms Tibbetts' were earlier found in a cornfield near her hometown of Brooklyn.
The 20-year-old University of Iowa student went missing on 18 July while dog-sitting at the home of her boyfriend and his brother.
She was last seen by neighbours on a run. Her family reported her missing the next day when she did not arrive at work.
Iowa Division of Criminal Investigations special agent Rick Rahn said in a press conference Mr Rivera is an undocumented immigrant from Mexico.
Mr Rivera allegedly saw Ms Tibbetts running and followed her before he says he "blacked out".
"I can't speak about the motive," Mr Rahn told reporters.
"I can just tell you that it seemed that he followed her, seemed to be drawn to her on that particular day, for whatever reason he chose to abduct her."
Mr Rahn said Mr Rivera was "very compliant" and willing to talk, and said that he led police to her body.
An arrest warrant says Mr Rivera is charged with murder in the first degree. He would receive a mandatory life sentence if convicted.
Authorities were led to the body in the early hours of 21 August, in a cornfield in Poweshiek County - which includes Ms Tibbetts' Brooklyn hometown.
The body had corn stalks placed on top of it, Mr Rahn told reporters.
A surveillance video of Ms Tibbetts jogging, and of Mr Rivera's car, helped authorities track the suspect down, he said.
Police received more than 4,000 tips during their 34-day investigation.
After the arrest, President Donald Trump told an audience at a rally in West Virginia the crime "should have never happened".
"You heard about today with the illegal alien coming in very sadly from Mexico," he told the crowd.
"And you saw what happened to that incredible, beautiful young woman."
Mr Trump called on his fellow Republicans to sweep the midterm elections in November in order to strengthen immigration laws.
Both of Iowa's Republican senators urged Congress to pass a law requiring Immigration and Customs Enforcement to take custody of any undocumented migrant who is charged with a crime that results in serious injury or death.
"No family should ever have to endure such a tragedy, especially one that could have been prevented," said Senators Chuck Grassley and Joni Ernst.
"Too many Iowans have been lost at the hands of criminals who broke our immigration laws. We cannot allow these tragedies to continue," they added.
Republican Iowa Governor Kim Reynolds said in a statement: "We are angry that a broken immigration system allowed a predator like this to live in our community, and we will do all we can to bring justice to Mollie's killer."