That contest is the fourth international game confirmed for the 2018 season, with three slated to be played in London.
The date and time of the game in Mexico City will be announced during the offseason.
"Over the past two seasons, we have seen the extraordinary passion that exists for NFL football in Mexico," Goodell said in a statement. "We are excited for another memorable event at Estadio Azteca as the Los Angeles Rams and Kansas City Chiefs head to Mexico City in 2018."
Rams owner Stan Kroenke is looking forward to traveling south of the border for the game.
"Southern California and Mexico share strong historic and cultural ties and this game will provide an opportunity to celebrate the special connection between these two regions," Kroenke said. "It is great to be participating in the NFL's international games again and working with the league to grow the game abroad. Mexico has one of the largest NFL fan bases in the world and we are excited to bring Rams football to the millions of fans there."
Chiefs owner Clark Hunt is excited to see his team play in its first regular-season game in Mexico. The Chiefs competed in a preseason contest in Monterrey, Mexico, in 1996.
"We are thrilled to be a part of the NFL's international initiatives once again, and we are excited to face the Rams at historic Estadio Azteca this fall," Hunt said. "The support for the NFL in Mexico has grown significantly since our initial trip in 1996. We look forward to returning to Mexico and connecting with a new generation of fans this season."
As for the other international games, the Seattle Seahawks and Oakland Raiders will kick off the festivities in England on Oct. 14 at the new Tottenham Hotspur stadium. The Philadelphia Eagles will play the Jacksonville Jaguars while the Tennessee Titans will challenge the Los Angeles Chargers, with both games to be contested at Wembley Stadium.
The order of the latter two games -- Oct. 21 and Oct. 28 -- will be announced closer to the season.