News of the arrests came from Phuket Governor Tri Augkaradacha on Monday morning during a meeting with local officials and tourism industry representatives.
The meeting, also attended by members of the Phuket Provincial Administration Organization, was held to arrange a much larger gathering, scheduled for Wednesday, to discuss tourist safety issues in Phuket.
Further details about the identity of the two men and how police were able to track them down are expected to come at a police press conference after the suspects' return to the island.
Smith's companion, Tammee Lynn, 42, was also hurt and requied stitches.