Simpson was laid down at Bath Iron Works, Maine, on 27 February 1984, launched on 31 August 1984 sponsored by Mrs. Gloria Fowles-Simpson widow of Rodger W. Simpson and commissioned on 21 September 1985 in Newport, Rhode Island, Cmdr. H. Wyman Howard Jr. in command. The ship was delivered 13 September 1985. BIW plans called for delivery to occur 9 August 1985, but that date slipped due to an extended strike at Bath Iron Works that began 30 June 1985. Simpson was homeported at Naval Station Newport until switching to Naval Station Norfolk on 31 March 1994. Simpson moved to Naval Station Mayport in July 2001.
In January 1986, Simpson participated in search and recovery operations following the Space Shuttle Challenger disaster.
Beginning January 1988, Simpson's first overseas deployment was to the Persian Gulf as part of Operation Earnest Will, to escort reflagged Kuwaiti oil tankers during the Iran–Iraq War. On 17 April 1988, Simpson took part in Operation Praying Mantis, the U.S. response to the mining of the frigate Samuel B. Roberts, which hit an Iranian M-08 mine on 14 April 1988.
On 18 April, Simpson, along with Wainwright and Bagley, destroyed Iranian naval and intelligence facilities on the oil platform Sirri in the Persian Gulf. Later that day, the ships encountered the Iranian Kaman Class (Combatte II type) missile patrol boat Joshan, which launched a Harpoon missile. Simpson immediately returned missile fire, striking Joshan in her superstructure. Joshan was then sunk by combined gunfire. Simpson was awarded the Joint Meritorious Unit Award and the Combat Action Ribbon for this operation, and the Armed Forces Expeditionary Medal for the deployment.