The alligator is thought to be the one that attacked Tommie Woodward, 28, who jumped into a bayou early Friday morning -- despite a verbal warning from a witness and a posted "No Swimming Alligators" sign at Burkhart's Marina in Orange County.
It is believed to be the first alligator attack on record in Texas.
The body of an alligator was found Monday on a boat ramp near the site of the attack, according to the Texas Wildlife and Parks Department.
Kent Robnett tells CNN affiliate KTRK
that he trapped the 400 pound, 11½-foot alligator himself and then shot it in the head. He left the carcass on the marina dock where officials recovered it.
"This was a truly horrific tragedy that unfortunately became compounded by the actions of an individual who felt compelled to take matters into his own hands for the safety of his family and others," said Col. Craig Hunter, law enforcement director for the Texas Parks and Wildlife Department.
Though an autopsy reported that Woodward died by drowning, Orange County Justice of the Peace Rodney Price says his body parts were found inside the alligator.
Robnett told KTRK that he killed the deadly creature to protect his family and others who walk and swim near the bayou, which is near the Louisiana state line.
"I have a 1-year-old, a 3-year-old and a 14-year-old who swim out here," he told the affiliate. "He was just too big."
Robnett says he knew he was breaking the law and anonymously called a game warden, knowing he could face a charge of hunting without a permit and a $500 fine. He has since talked to investigators.
"Either Texas game wardens or a licensed nuisance alligator hunter would have been more appropriate to handle the situation. Either way, because of its aggressive behavior, the alligator would have to be killed," said Hunter.
Robnett was issued a warning but will not be charged, Hunter said.
In last week's incident, Woodward seemed to mock the deadly creatures. Justice Price told CNN affiliate KFDM
that "he said 'blank the alligators' and jumped into the water and almost immediately yelled for help."
Woodward's body was found hours later. An unidentified woman who jumped in with him for the late-night swim was not injured.