The coalition said its forces had "cleansed Great Hanish", an island in the archipelago, which is situated near the Red Sea's main shipping lanes.
The area had been subjected to weeks of heavy shelling by Arab forces before they were seized, according to Reuters.
In September 2014, the area was captured by Houthi militia fighters from forces loyal to the ousted Yemeni President, Ali Abdullah Saleh.
The islands were apparently used for storing weapons and smuggling them into Hodeida, Yemen's main Red Sea port.
The archipelago was the subject of a territorial dispute between Yemen and Eritrea, which seized the islands in the 1990s and held them until a London-based international arbitration court granted Yemen sovereignty in 1998.