KVUE-TV reports that Austin police had one person - identified as Kendrex White - in custody after the Monday afternoon stabbing.
Campus classes and events were canceled for the day but will resume Tuesday.
UT police said that after responding to the scene, they found White with a large "Bowie-style hunting knife". Austin Police say one died and three others were left injured.
The first person attacked was one of several students gathered around a popular Austin food truck around 2 p.m.at the plaza outside Gregory Gym, one of the busiest areas on the 431-acre campus.
It was unclear why White allegedly targeted the four students, who Carter did not identify but said were in their early 20s.
Prichett said the attacker had escaped attention by blending in.
In a matter of minutes, UT police say, biology junior Kendrex J. White, 21, stabbed four students - killing one and injuring three.
According to The Tab, those who attended UT Austin warned each other not to display Greek letters in the wake of the attack, with some claiming that additional students were targeted for belonging to Greek groups.
He also saw first responders who were trying to resuscitate one of the wounded students, but Arredondo said he had a sense that it was too late and the student had already expired, he told the Amarillo Globe-News in a telephone interview.
The attack occurred a short walk away from a landmark clock tower that was the scene of a mass shooting in 1966.
Ex-classmate Angela Bonilla called White "the sweetest guy, laughing and having a good time with people".
"While I was running away, I saw this other guy that was kind of bloodied up sitting at a table slumped over".
While UT continued to say that there are no threats to campus Monday night, they did continue extra police patrols and extended bus line hours.
"I was a little terrified of being in that building, but my teacher was extremely understanding, she let us turn in our assignment and walk out", Garza said.
Friends close to White said he was an active volunteer in organizations on campus.
A former high school classmate of White's said she was surprised to see he was the person arrested.
White is now being detained at police headquarters and there is no known motive at this time.
According to an arrest affidavit, police arrested White on April 4 on a charge of driving while intoxicated after he was involved in a wreck on campus.
"This breaks my heart to have to announce this, that any of our students are touched by tragedy", Greg Fenves, the university's president said at a news conference. This would have fell within timely warning because there was no ongoing threat.
"Our prayers go out to all those affected by today's tragic events", Texas Gov. Greg Abbott said in a statement after the attack.
Stabbing on University of Texas at Austin campus.