The two nations will meet on June 2 at the 46,000-seater stadium, which was previously home to the Washington Redskins and, until last year, Major League Soccer team DC United.
The intention for both parties is to reach a new audience in a country where rugby's popularity continues to grow.
"The match in Washington allows us to take Springbok rugby to America and potentially expand the team's appeal to a very large audience," says Jurie Roux, head of the South Africa Rugby Union.
"Our research shows that the Springboks have a growing worldwide fan base and we see the match in Washington as an ideal platform to tap into a market that offers huge possibilities for South African rugby, in the exciting American sporting area."
The seven-a-side game has proved particularly popular in the US. The Las Vegas leg of the Sevens World Series has, in recent seasons, attracted over 80,000 spectators across three days of competition.
Sevens will get a further boost when San Francisco plays host to this year's World Cup in July.
Major League Rugby -- being billed as the highest level of American club rugby -- kicks off in 2018 and will feature seven teams in its inaugural season with an eighth to be added in 2019.
The match between South Africa and Wales will not be the first high-profile international to move state-side. Ireland and New Zealand
met at Chicago's Soldier Field in front of a sold-out crowd of 61,000 in 2016. It was a game that saw Ireland overturn the All Blacks' 18-match unbeaten run.
"This is an exciting fixture for the WRU and for the national squad," says Welsh Rugby Union CEO Martyn Phillips. "It is a great opportunity to showcase Wales and our game in the capital of the United States.
"The opportunity to expand the already great Welsh support base and Welsh brand is very exciting for us, especially in such a large demographic and audience as the US."
Wales will then go on to face Argentina in Santa Fe and San Juan as part of the side's preparations for next year's World Cup in Japan.
The most recent encounter between South Africa and Wales was in Cardiff in December last year, with the hosts winning 24-22.
The Springboks have recently parted ways with coach Allister Coetzee, who led the side to just 11 wins in 25 games, and signed former player Rassie Erasmus on a five-year contract running until the 2023 World Cup. The two-time world champions sit sixth in the world rankings.
Wales, meanwhile, is one spot below its Southern Hemisphere rival. After a convincing victory over Scotland in the opening weekend of the on-going Six Nations Championship, it has fallen to defeats by England and Ireland in the two most recent rounds.