Police said Stephen Broderick, 41, was arrested without incident around 7:30 a.m. along a rural road in Manor, an Austin suburb, Manor Police Chief Ryan Phipps said. He had a pistol in his waistband, Phipps said.
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Police had received two phone calls about a suspicious person matching Broderick's description, Phipps said.
Interim Austin Police Chief Joseph Chacon said Broderick was suspected in Sunday's deaths of two women and one man, all of whom Broderick knew.
Police initially told Austin residents who lived nearby to shelter in place, but they lifted that request later Sunday when they said it was unclear whether Broderick was still in the city.
Chacon said that Broderick was a former deputy with the Travis County sheriff's office, which is based in Austin.
Travis County District Attorney Jose Garza said in a statement that Broderick had been arrested for sexual assault of a child last June and was released on $50,000 bond. He said that the district attorney's office on Sunday filed a motion to revoke that bond.
Sheriff's spokeswoman Kristen Dark told the Austin American-Statesman that Broderick, a property crimes detective, resigned after the arrest.
The newspaper also reports that Broderick's wife filed for a protective order and divorce shortly after his arrest.