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The initial shooting happened shortly before noon on Stella Link Road, just north of the South Loop.
The sheriff's office said Deputy Jesus "Jesse" Vargas was taken to Ben Taub Hospital, where he died.
Authorities said Vargas served the Brazoria County Sheriff's Office for 17 years. He leaves behind a wife and three children.
A manhunt continued for nearly five hours until the suspect, identified as Robert Lee Davis, aka Sean Christopher Davis, was shot and killed by law enforcement.
Sources told Eyewitness News that he was hiding in a dumpster in an alleyway near the initial shooting.
Shortly after authorities conducted a news conference, a "Blue Alert" was sent across the state in search for Davis.
"This afternoon, we lost a local hero," Mayor John Whitmire said. "(Vargas) attempted to apprehend a repeat violence offender, and he lost his life. The suspect shot (Vargas) as he approached him to serve the warrant."
During the shooting that killed Davis, a K-9 officer was injured, and a DPS helicopter rushed the officer to the Westbury Animal Hospital.
Records show Davis has a criminal history dating back to 1990, the most recent being from December 2024 for aggravated sexual assault charges against a relative.