According to charging documents, 37-year-old Bruce Butler is accused in the deaths of 38-year-old Richard Nugent and 66-year-old RJ Lewis.
On June 20, the Houston Police Department released surveillance photos of a person of interest, later identified to be Butler.
Records show a tip led to Butler's arrest on Monday when he allegedly admitted to his role in the shooting.
He was charged with capital murder and booked into the Harris County Joint Processing Center.
Records show Butler is homeless and has a criminal history, including car burglaries and assault causing bodily injury.
SEE MORE: Person of interest wanted in shooting death of man and woman near Buffalo Bayou Trail, HPD says
On June 2, officers said they found Nugent's body on the sidewalk near Buffalo Bayou Trail. While officers were canvassing the area for witnesses, they also found Lewis lying on a stairwell leading up to the intersection of Congress and Smith Streets.
Houston Fire Department paramedics pronounced both victims dead at the scene.
At the time, there was no known motive for the deadly shootings.
SEE MORE: Investigation underway after man and woman's bodies found near Buffalo Bayou Trail, HPD says