U.S. Magistrate Judge Jacqueline Chooljian issued her ruling Tuesday after an extradition hearing in Los Angeles.
Beresford-Redman appeared in court in a jail jumpsuit and was shackled throughout the hearing. He did not react during the hearing.
Beresford-Redman has been in jail since November when U.S. authorities arrested him on a fugitive warrant out of Mexico. He's accused of murdering his wife, Monica, at a resort in Cancun in April 2010 and placing her body in a sewage cistern.
An autopsy says she was struck on the head and asphyxiated.
According to the extradition treaty with Mexico, prosecutors only have to show that there was probable cause that he killed his wife on a family vacation. The magistrate said there was, despite the defense's contention that the evidence does not add up.
Beresford-Redman's defense team had hoped to put on the stand his 6-year-old daughter, who had responded to attorneys' questions about that night in April when there were loud noises coming from the family's hotel room.
An assistant U.S. attorney laid out the evidence gathered by Mexican investigators: hotel guests reported screams like a woman in distress and sounds of furniture being dragged across the floor.
Beresford-Redman told investigators his family was playing a game. His daughter told her therapist what happened in response to questions posed by the defense. "Mommy and Daddy did not yell at each other and never hit each other," she said.
Tuesday morning though, the defense decided to not to call the child to the stand.
The body of Monica Beresford-Redman was found in a wastewater cistern days after Bruce says she went on a shopping trip.
Blood was found in the room, but the defense says it did not belong to either Bruce or Monica. The defense argued the evidence was conflicting.
"Mexican forensic people conclude there are two separate ways in which Ms. Beresford-Redman died, two different times of death," said defense attorney Richard Hirsch.
Prosecutors cited a long list of circumstances, including Bruce's affair with another woman, whom he continued to call from Mexico.
There was a delay in reporting his missing wife. Scratches were found on his neck. He flew from Mexico back to the U.S. without notifying Mexican authorities. Now he must return.
"Pursuant to the extradition treaty, the fugitive will now be tried in Mexico under the standards employed in Mexico," said Assistant U.S. Attorney Justin Rhoades.
Defense attorneys say they will file appeals. Depending on the outcome, it could be weeks or even years before Beresford-Redman goes to trial in Mexico.