During the late 1950s, the RAN announced a requirement for guided missile-armed warships; along with plans to install guided missiles aboard currently active escort vessels, plans were made to acquire two purpose-built destroyers. Although traditionally, Australian warships were based on British designs, the RAN chose to study the United States Nay's Charles F. Adams class along with the Royal Navy's County class. The American design was favoured because the Tartar missile carried was seen as superior to the British Sea Slug, but the risk of operating American-designed ships in a predominately British-designed naval force was seen as acceptable after a RAN proposal to redesign the County's combined steam and gas propulsion system to purely steam-powered was knocked back by British. In 1960, the decision was made to instead acquire Charles F. Adams class ships, and on 6 January 1962, two destroyers of a slightly modified design were ordered from Defoe Shipbuilding Company of Bay City, Michigan. Plans to refit Tartar missiles to the Battle and Daring classes were later cancelled because of cost, and on 22 January 1963, a third destroyer was ordered from Defoe. The Australian ships were referred to as the Perth class after lead ship HMAS Perth; the other two destroyers were HMA Ships Hobart and Brisbane. Thought was given to acquiring a fourth ship of the class, but this did not go ahead.
At launch, the destroyers had a standard displacement of 3,370 tons, and a full load displacement of 4,500 tons, although by 1998, various modifications and modernisations had increased the ship's full load displacement to 4,618 tons. Each ship was 440.8 feet (134.4 m) long at the waterline, 437 feet (133 m) long overall, had a beam of 47.1 feet (14.4 m), and a draught of 20.1 feet (6.1 m). The propulsion system consisted of four Foster Wheeler D-type boilers connected to two General Electric double reduction steam turbines; these provided 70,000 shaft horsepower (52,000 kW) to the two propeller shafts, allowing them to reach speeds of 35 knots (65 km/h; 40 mph). Maximum range was 6,000 nautical miles (11,000 km; 6,900 mi) at 15 knots (28 km/h; 17 mph), or 2,000 nautical miles (3,700 km; 2,300 mi) at 30 knots (56 km/h; 35 mph). The standard ship's company at launch consisted of 21 officers and 312 sailors.
Construction of lead ship Perth commenced when she was laid down on 21 September 1962. Perth was launched on 26 September 1963, completed on 22 May 1965, and commissioned into the RAN on 17 July 1965. Hobart was laid down a month after Perth on 26 October 1962, with launching on 9 January 1964, and completion on 18 December 1965, two days after she was commissioned into the RAN. Work on Brisbane did not start until 15 February 1965, with the destroyer launched on 5 May 1966, commissioned on 16 December 1967, but not completed until 24 January 1968. Construction and acquisition of the Perth class included many firsts for the RAN: they were the first ships to be armed with guided missiles, the first to be designed and built in the United States, and the first to be launched sideways instead of stern-first. During construction, the ships were respectively identified with the United States Navy hull numbers DDG-25, DDG-26, and DDG-27.