Antonio Collins, 32, of Charleston was arrested Saturday evening in Columbus, Ohio, by a U.S. Marshal task force.
Officers started searching Charleston for Collins, also known as "Shake," after Lawson and Moore were shot about 3:15 a.m. Saturday.
Cooper said Collins had help from friends in traveling to Columbus. He said Collins is associated with other violent criminals who also are known to police.
"I'm sure that they aren't surprised to hear that they are also under investigation and we are watching them as well," Cooper said.
He said officers received information on Collins' whereabouts Saturday while searching for him. They passed that information on to the U.S. Marshals Office.
"We can't say specifically what we know about his reason for going to Columbus other than clearly part of that was to flee apprehension, to hide," Cooper said. "It's not uncommon after a major violent crime is committed for the perpetrator to leave the area, and Columbus is a popular destination for those on the run from Charleston."
Cooper said the federal marshals assisted in the search because of the violent nature of the crime, the extreme danger presented to the public and because Collins was previously convicted on federal charges.
Authorities working with the U.S. Marshal's Southern Ohio Fugitive Apprehension Strike Team (SOFAST) were able to find and arrest Collins quickly, Cooper said.
Collins is being held in Columbus until he can be extradited back to Charleston, where he will face two counts of attempted murder.