He has been charged with three counts of murder, three counts of aggravated assault and two counts of kidnapping, the chief added. Cox said Rhoden was the lone shooter in the killings.
Rhoden was arrested in the Chamblee, Georgia, area and “has ties to the metro Atlanta area,” Cox said.
“We literally had detectives that have worked around the clock and some have literally slept in their offices since July 3 trying to clear this case,” he added.
Rhoden’s name came up “within a few days” since the start of the investigation, the chief said.
Investigators are now exploring the relationship between Rhoden and his victims, the chief said, adding “we definitely feel confident there was no relationship between the shooter and Mr. Siller.”
This remains an active investigation, the chief said.
What police said about the killings
Police previously said they were called to a report of a person shot on Saturday afternoon and found Siller — who was the club’s director of golf — shot in the head near the green of the course’s 10th hole.
A truck was on the green, and officers found the bodies of the two other men in the truck’s bed — both of whom also had been shot, police said. One of the slain men was Paul Pierson, 76, of Kansas — the registered owner of the Ram 3500, police said.
Police identified the third victim as Henry Valdez, 46, of California, and said he and Pierson appeared “to have no relation to the location at all.”
Someone had driven to the green in the truck — a white Ram 3500 pickup — and shot Siller when Siller arrived to see what was going on, a member of the club told CNN affiliate WXIA. The shooter then fled, WXIA reported.
On Tuesday, police said they believed Siller was killed “because he witnessed an active crime taking place.”
“It does not appear he (Siller) was targeted,” but instead was killed because he “happened upon a crime in progress involving the unknown suspect and the two deceased males,” the Cobb County police said in a news release.
Siller, 46, leaves behind a wife and two children, ages 6 and 7, according to the Pinetree Country Club.
CNN’s Christina Maxouris, Jason Hanna and Gregory Lemos contributed to this report.