He said he dragged her 60ft (20m) into a secluded corn field, and allegedly left her body face-up and covered with corn plants.
"You saw what happened to that handsome, incredible young woman".
The body of Ms Tibbetts, who went missing on 18 July, was discovered by investigators on Tuesday after they were led to the scene by Mr Rivera.
Rivera, a 24-year-old Mexican man who officials said came to the USA illegally, largely remained silent in court, answering yes or no questions in Spanish through an interpreter. Rivera next remembers seeing her earphones on his lap, and taking her bloody body out of the trunk of his vehicle, it said.
But according to federal immigration officials, Rivera is in the country illegally.
The government is incorrectly promoting the idea that Rivera is not in Iowa legally, attorney Allen Richards of Tama said in a court document asking for a gag order in the case.
But Mr Rivera's farm employers said he had passed an immigration background check.
"You heard about today with the illegal alien coming in, very sadly from Mexico, and you saw what happened to that incredible, attractive young woman?"
The lawyer asked the court to prevent the government from claiming Rivera is in the country illegally. "We're getting it changed but we have to get more Republicans".
Willian enjoying Chelsea's 'Samba style' under Sarri
"I like the boy [Sarri] has brought in, Jorginho, I think he has been absolutely outstanding", Wise told Goal . He's one of the best players we've ever seen in the Premier League, and bringing him back was a masterstroke.
Law enforcement officials Tuesday said he was an undocumented immigrant, which immediately fueled political debate, including comments from President Donald Trump and Iowa Gov. Kim Reynolds. Similarly, a study from Northwestern University found no correlation between immigrants and violent crime. In fact, some have shown that undocumented immigrants are less likely to commit crimes than native-born citizens.
That hasn't stopped people from seizing on another powerful anti-immigration anecdote.
Williams showed viewers the Brooklyn, Iowa, neighborhood where the 20-year-old University of Iowa was last seen alive.
The killing has recharged the USA debate over illegal immigration after it emerged the suspect was Mexican.
Investigators believe Rivera abducted Tibbetts while she was out on a jog July 18.
It showed Tibbetts jogging and Rivera's auto - and was a critical clue in identifying a suspect.
Rick Rahn, special agent in charge at the Iowa Division of Criminal Investigation, said the suspect's motive was unclear.
An autopsy is scheduled Wednesday by the state medical examiner to determine the cause of death.
They thanked "all of those from around the world who have sent their thoughts and prayers for our girl".
Trump has often suggested, erroneously, that undocumented immigrants are more unsafe than United States citizens.