Major League Baseball matches have already been staged outside the United States of America in Mexico, Japan, Puerto Rico and, most recently, at Australia's Sydney Cricket Ground in March 2014.
The league then wants to return in 2020 and establish "a long-term footprint in the city". "This is our most significant endeavor ever in Europe, and we look forward to showcasing Major League Baseball in one of the world's great cities".
The 2019 matches are set for June 29-30, with the Red Sox designated as the home team, in what will be the first regular-season Major League Baseball fixtures staged in Europe. The Yankees opened the 2004 season with a two-game series against the Rays and the Red Sox opened the 2008 season with two games against the Oakland Athletics.
Mr Khan has said he wants to make London the sporting capital of the world.
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Hal Steinbrenner, Yankees' managing general partner, said: "Bringing these storied teams together for British fans - who have such a profound appreciation for sports at the highest level - only adds to the unique allure of one of the world's greatest sporting rivalries. I can't wait to hear someone shout "play ball" at London Stadium".
Major League Baseball is following American football and basketball in crossing the Atlantic.
Major League Baseball had planned to host regular-season matches in London in 2017, but these were abandoned due to time constraints.
"London Stadium has a track record of successfully delivering major global events, moving from Premier League Football and both worldwide and domestic showpiece rugby fixtures to hosting some of the biggest names in music".