The historic meeting between the New York Yankees and Boston Red Sox at London Stadium will be shown live on the BBC iPlayer and BBC Sport website.
The games on 29 and 30 June are part of a two-year deal signed by Major League Baseball and BBC Sport to stream the London Series in the United Kingdom.
They will be the first two MLB games to be played in Europe.
The NBA and NFL already stage regular-season basketball and American football fixtures in London.
"We're very excited to bring the MLB London Series to free-to-air audiences across the country for the first-ever time this summer," said Victoria Cotton, BBC Sport Live Streaming Executive Editor.
"Our digital platforms are proud to provide coverage of world-class sporting entertainment and MLB will bring a new level of interest to our channels."
The Oval cricket ground was reportedly considered as a possible venue, before organisers settled on London Stadium.
They plan to lay a protective cover over the top of the current pitch - used by West Ham - and install a fresh surface over the top.
The participating teams in the 2020 London Series are yet to be announced.
The MLB has already taken games to Mexico, Japan and Australia
Meanwhile BT Sport has extended its agreement to show regular-season and post-season games through to 2021.