The move means, when Virginia investigators arrive, he can be taken back to their state, Eyewitness News' Tracy Clemons reports.
Matthews was taken into custody Wednesday night in Gilchrist after a nationwide search.
Matthew, 32, went before a magistrate judge for the first time Thursday morning, after being arrested on a Galveston County beach. He was not required to enter a plea but was denied bond.
"He had the charge out of Virginia which is abduction of a person with intent to defile," said Galveston County magistrate Judge Mark Henry. "He had a Galveston county charge for failure to ID or giving false information."
The FBI and police in Charlottesville, Virginia, had been looking for him in the disappearance of 18-year-old Hannah Graham. The University of Virginia student vanished September 13 after last being seen in surveillance video at a mall near the university.
Days later, Matthew was questioned by police and later vanished. But yesterday at around 3:30pm, that all changed when Galveston County sheriff's deputy Ross Perez got a call about a suspicious person on a beach in Gilchrist.
"Stopped by the individual on the beach that we all know is now in the Galveston County Jail, trying to identify him," said Galveston County Sheriff Henry Trochesset.
"They took all my clothes," said Matthew while in magistrate court.
Matthew asked about when he'd get his clothes back and why he had to sleep on a hard surface.
The magistrate asked Matthew to sign several papers indicating whether he was requesting a court-appointed lawyer and whether he was claiming he was not the person identified on the Virginia fugitive warrant.
"What does this mean?" Matthew asked at one point while looking at the paperwork.
As the magistrate explained what he was being asked to sign, Matthew interrupted him saying, "What? I'm sorry."
When the magistrate finished his explanation, Matthew asked, "And if I sign it?"
"I read him his rights as I did ever other defendant in the county jail this morning," said Judge Henry. "Virginia denied his bond. I let him know about that. He declined a court appointed attorney."
Meanwhile, FBI and law enforcement out of Virginia are headed to Galveston to see Matthew. And because of the sensitivity of this case, very few details can be release.
"At this time, our communication with law enforcement in Virginia and the FBI out of Virginia and locally here, they're asking us to please not give certain particulars of the case out, and at this time, I'd like to honor that," said Trochesset. "At some time today, investigators from Virginia will arrive here in Galveston County and we'll move forward from there."
The vehicle Matthew was in is now in custody.
As for the search for Graham, she has still not been found.