Nash had told WGCL-TV in Atlanta she was concerned because Daniel Cleary had purchased a firearm about a month ago, was under stress and drinking.
Police said they did not know if Daniel Cleary was in possession of a firearm when he was taken into custody.
McGee said authorities will arrange for Daniel Cleary's extradition to Georgia. He faces a charge of interstate interference with custody, a felony. McGee said police will discuss with prosecutors whether other charges will be brought.
Police on Friday had released surveillance footage showing the two missing boys at a Walmart in Tennessee on Dec. 23 and 24 with their father. Though initial reports were that the Walmart was in Jackson, McGee said it was in fact in Chattanooga.