Yost's extension keeps him under contract through the 2018 season. The length of Moore's extension wasn't revealed.
The duo are the architects of a Kansas City team that has played in back-to-back World Series. The Royals defeated the New York Mets in last season's World Series and lost to the San Francisco Giants in 2014.
"We are extremely delighted that Ned will remain our manager through at least the 2018 championship season," Moore said in a statement. "It's an absolute joy and honor to work alongside him."
The contracts of Yost and Moore were both set to expire after this season before the organization worked out the extensions.
Royals president Dan Glass made it a priority to retain Moore and raved about his abilities.
"You can't find an individual with a stronger work ethic or dedication to his craft than Dayton Moore," Glass said in a press release. "He possesses all of the qualities you look for starting with his leadership, to organizational vision and tireless dedication to the position. Dayton also possesses the ability to get everyone working toward the same common goal, which is to strive daily to make this organization better."
Yost has more wins than any manager in Royals' history. He has a 468-469 record in six seasons with the club.
The Royals have won 86 or more games in each of the past three seasons. Kansas City was 95-67 last season en route to winning its first World Series since 1985.
Yost also managed the Milwaukee Brewers from 2003-08. His career record is 925-971.