Built in 1951, the airport was served in the 1950s by Alaska Airlines, Northwest Orient, Pacific Northern Airlines and Reeve Aleutian Airways, using aircraft ranging from Douglas DC-3s to Boeing 377s, and was also a refuelling stop for Canadian Pacific Air Lines service to the Far East (one such aircraft being involved in a 1951 disappearance). From 1955 to 2011, the eastern end of the airport's southernmost runway connected to the Kulis Air National Guard Base.

By the mid-1980s the airport's nickname was "Crossroads of the World". Anchorage was a common stopover for passengers flying between Europe and East Asia, because airspace in China, the Soviet Union and Eastern Bloc countries was off-limits and because the first generation of jets and widebody airliners did not have the range to fly non-stop across the Pacific Ocean. Carriers using Anchorage for this purpose included:

Air France, British Airways, Iberia, KLM, Lufthansa, Sabena, Swissair and Spantax all used Anchorage as a stopover point between Europe and the Far East of Asia into the 1980s to 1991.

Japan Airlines served Seattle through Anchorage in the early 1960s, and offered service through Anchorage to London, Paris, Amsterdam, Copenhagen, Düsseldorf, Hamburg, New York City & São Paulo from the 1960s until October 1991. Last JAL flight was JL438 on October 31, 1991, Paris–Charles de Gaulle - Anchorage - Tokyo–Narita.

Korean Air used Anchorage as a stopover point for flights between Seoul and both Europe and the continental US in the 1980s. On September 1, 1983, one of these flights, Flight 007 was shot down by a Soviet pilot who had mistaken it for a spy plane, after unintentionally violating Soviet airspace.

Northwest Orient, the first airline to operate scheduled trans-Pacific service after World War II, used Elmendorf Field and later Anchorage International as a stopover for service between US points (Seattle, Chicago and Minneapolis at various times) and Tokyo as late as the mid-1970s.

Scandinavian Airlines (SAS) began a transpolar flight from Copenhagen to Tokyo via Anchorage on February 24, 1957.

In the mid-1980s airport officials knew that the then-new Boeing 747-400, with a longer range than then-existing aircraft, would decrease stopovers. They did not expect that Mikhail Gorbachev's glasnost, towards the end of the Cold War, would open Soviet airspace to flights, causing the decrease to occur sooner than planned. By 1988, 16 airline flights that had previously stopped in Anchorage—each bringing almost $80,000 in revenue to the state—instead flew nonstop over Siberia.

Most scheduled passenger service from Anchorage to Europe and Asia ceased in the early 1990s. Korean Air continued to serve Anchorage three times a week on a yearly scheduled basis until March 2005, which was reduced to three times a week only for the summer season in 2006. China Airlines, the last Asian carrier to serve Anchorage on a regular basis, used Anchorage as an intermediate stop on its Taipei-New York route until 2011, when it rerouted these flights to stop in Osaka. While a few charter passenger aircraft still stop at Anchorage on flights between Asia and the eastern United States, scheduled cargo carriers – which benefit from more volume and thus shorter route segments – continue to use Anchorage frequently. Condor still uses the Frankfurt-Anchorage route on a Airbus A330neo.

In the 1990s, Alaska Airlines and Aeroflot operated services from Anchorage to several destinations in the Russian Far East, including Khabarovsk, Magadan, Petropavlovsk, Vladivostok and Yuzhno-Sakhalinsk. Alaska Airlines pulled out of these markets in 1998 due to insufficient demand, while the Aeroflot services were primarily intended as technical stops en route to Seattle and San Francisco and were cancelled once newer aircraft and nonstop flights became available. Reeve Aleutian Airways, Dalavia and MAVIAL Magadan Airlines also offered service between Anchorage and the Russian Far East at various times, catering to Kamchatka oil exploration and other niche markets.

The airport was renamed in 2000 by the Alaska Legislature to honor then long-standing US Senator Ted Stevens. Stevens survived a crash at the airport in 1978 that killed his wife Ann.

In October 2018, Alaska Governor Bill Walker and Heilongjiang Province Governor Wang Wentao announced plans to connect Anchorage and Harbin Taiping International Airport with year-round, nonstop flights as early as the summer of 2019.

On November 30, 2018, the airport suffered minor damage and was temporarily closed following a magnitude 7.0 earthquake in the area. In June 2019, American Airlines switched the Boeing 737-800 on their seasonal route to Phoenix with the Airbus A321neo making them the first airline to use the A321neo at Anchorage. In January 2023, Delta replaced their Boeing 737-900 and 757-200 in favor of the A321neo for their route to Minneapolis-St.