The Red Sox and Yankees are now the best two teams in the Major League Baseball, with 25 and 24 wins respectively.
The London Stadium hosted the opening and closing ceremonies of the 2012 Olympic Games.
The NFL has played regular-season games in the capital since 2007, holding 18 games at Wembley and three at Twickenham. "We are bringing you one of the best rivalries in baseball". Two games in London, next June 29th and 30th.
The NBA and National Hockey League have also held regular-season games in London.
"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".
Cleveland and Minnesota played a two-game series last month in San Juan, Puerto Rico, and the Los Angeles Dodgers and San Diego played in a three-game series in Monterrey, Mexico, last week.
Major League Baseball also announced that the Oakland Athletics and Seattle Mariners will open next season at the Tokyo Dome on 20-21 March.
Steinbrenner added: "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".
London will host three National Football League games this season, with the Philadelphia Eagles facing the Jaguars at Wembley and the Tennessee Titans taking on the Los Angeles Chargers at the same venue, while the Oakland Raiders and the Seattle Seahawks will face off at the soon-to-be-finished Tottenham Hotspur Stadium on 14 October.
The arrival of the game in London follows talks with Sadiq Khan when he became mayor in 2016.