"It's cool, man," Randolph told the Memphis Commercial Appeal. "This is where I want to be."
ESPN.com reported last weekend that the Grizzlies were working to complete a deal by July 1 to keep Randolph from reaching the open market. Sources close to the process said Friday that Randolph agreed to a two-year, $20 million extension -- which starts in 2015-16 -- after invoking his $16.5 million player option for next season.
Randolph, 32, averaged 17.4 points and 10.1 rebounds last season, helping Memphis win 50 games despite Marc Gasol's early-season knee injury in coach Dave Joerger's first season.
Randolph told ESPN.com as far back as November that he wants to play out the rest of his career in Memphis and hopes to establish a long-term relationship with the franchise similar to what divisional rivals Tim Duncan and Dirk Nowitzki have in San Antonio and Dallas, respectively.
The Associated Press contributed to this report.