Elliot got underway on 24 January 1977 for her maiden voyage, transiting from Pascagoula, Mississippi, to San Diego, California, via the Panama Canal.

On 24 September Elliot reported to Long Beach Naval Shipyard for a six-month restricted yard availability during which her NATO Sea Sparrow and Harpoon missile systems were installed.

Elliot departed for her first deployment, a seven-month Western Pacific tour, on 21 February 1979 as flagship of DesRon 31 in company with the aircraft carrier Ranger.

Elliot then joined a battle group centered around Midway and participated in operations in the Gulf of Aden to maintain a U.S. military presence in the area.

Port visits on this deployment included stops in Hawaii, Guam, Korea, Thailand, Hong Kong, Philippines, Japan, and Singapore.

Elliot reported to Todd Pacific Shipyard in Seattle, Washington on 17 August for the first private sector overhaul ever conducted of a Spruance-class destroyer.

"Elliot" and all Soviet combatant ships were at a continuous state of General Quarters (Battle Stations), with deck weapons ready to fire.

Shortly after departing this facility, Elliot struck a subsurface obstruction in the Seal Beach channel, causing some limited damage to the underwater hull and the starboard propeller.

On 30 April, Elliot proceeded to the Todd Shipyard facilities in San Pedro, California for repairs to her starboard propeller and sonar dome.

In May 1986 Elliot began a two-month selected repair availability which included installation of flight deck modifications necessary to support LAMPS Mk III helicopter operations.

Elliot departed San Diego on 9 September 1989 to participate in PACEX-89, said to be the largest major naval exercise in the Pacific since the close of World War II.

Ports visited included Pearl Harbor, Hawaii; Pusan, Korea; Subic Bay, Philippines; Singapore; Pattaya Beach, Thailand; Diego Garcia, BIOT; Muscat, Oman; Fremantle; and Hong Kong.

While transiting the South China Sea on 20 April 1990, Elliot rescued 35 Vietnamese refugees left adrift in a derelict boat and claiming to be the victims of pirates.

Elliot then entered the NASSCO yards on 9 September 1990 and remained there until 17 December, thus spending the majority of the Persian Gulf War on the sidelines.

Port visits were made to Pearl Harbor; Subic Bay; Phuket, Thailand; Bahrain; Oman; Abu Dhabi, UAE; and Hong Kong.

With the assistance of Elliot's air detachment the mine was safely detonated, resulting in a plume of water hundreds of feet tall.

Port visits on this deployment included Hawaii, Guam, Singapore, United Arab Emirates, Bahrain, Diego Garcia, Australia, and Fiji.

Elliot continued operating in this region into November, serving as anti-air warfare commander and Persian Gulf force over-the-horizon track coordinator for portions of this time period.

Elliot is now resting at a depth of 4,551 fathoms (27,306 feet (8,323 meters) in the Coral Sea, located at 24°43′S 155°50′E / 24.717°S 155.833°E / -24.717; 155.833, or roughly 100 nautical miles (190 kilometres) east of Fraser Island, Queensland, Australia.