Randolph's agent, Raymond Brothers, told Yahoo Sports on Friday morning that an agreement had been reached.
Randolph, 32, will exercise his $16.5 million player option for 2014-15 and extend the deal with the additional two years and $20 million. Randolph had until Monday to exercise his option or become a free agent on July 1. Talks had been ongoing for several weeks.
An extremely popular figure in the Memphis community, Randolph has expressed a strong desire to finish his career in the city where he has truly blossomed as a professional.
Randolph was essential in holding together a Memphis core that won 50 games and advanced to a Game 7 against Oklahoma City in the first round of the Western Conference playoffs.
Randolph has twice been an All-Star for the Grizzlies. He averaged 17.4 points and 10.1 rebounds this past season.