The deal will make him the highest-paid center in the NFL by average annual value. It includes $22 million guaranteed and an $11 million signing bonus, sources told Schefter.
Mike Pouncey, who is entering his fifth season with the Dolphins, had been due to earn $7.4 million in 2015, which was to be the final year of his contract.
Pouncey made his second consecutive Pro Bowl for Miami last season, despite missing four games to start the season with a hip injury. He also played all 12 games at guard for the Dolphins out of necessity, instead of his natural position of center.
The Dolphins plan to move Pouncey back to center in 2015 to anchor their offensive line. He has been a force for the Dolphins in four seasons, and the financial commitment keeps their 2011 first-round pick in Miami through the 2020 season.
Information from The Associated Press was used in this report.