Allen, 41, was making a routine traffic stop on Interstate 45, just south of Fairfield, Thursday, when Black allegedly shot him with a rifle and sped away.
Black is accused of shooting Allen.
"The tragic death of Trooper Damon Allen is a sad and sobering reminder of the risks our men and women in uniform take every day", said Governor Abbott. Allen died at the scene as police searched for Black using a helicopter, night vision goggles and lasers.
Roughly an hour later, authorities surrounded Black in a field and took him into custody.
Texas Governor Greg Abbott also chimed in, offering "prayers" for Abbot's family and justice for the dead man.
"Our DPS family is heartbroken tonight after one of Texas" finest law enforcement officers was killed in the line of duty, ' DPS Director Steven McCraw said in a statement.
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The trooper, who worked for the Texas Department of Public Safety, was killed around 4 p.m. local time. "Trooper Allen's dedication to duty, and his bravery and selfless sacrifice on this Thanksgiving Day, will never be forgotten".
DPS officials said they would file capital murder charges against Black, meaning prosecutors could potentially seek the death penalty in a state that has executed 518 people in the past 38 years.
It's not always easy for a trooper to return to his hometown straight out of recruit school, Barnes said; it can be hard for them to enforce the law in a place where they know nearly everyone.
"As close as we were, I had to hear about that from somebody else", he said.
In July, KYTX in Tyler reported Black was jailed in Smith County after a vehicle chase with deputies.
Smith County Court records show that the Lindale native was indicted by a Grand Jury there last month for aggravated assault against a public servant and evading arrest, both felonies.