The 29-year-old was nearing the end of his one-year contract with Memphis before the team offered a further two years for US$25 million (NZ$45 million), announced by the franchise today.
The 2.11m New Zealander led the NBA last season with 349 total offensive rebounds and 4.6 offensive rebounds per game, breaking the single-season franchise records previously set by Zach Randolph during the 2009-10 season.
He helped Memphis top the league with 18.6 second chance points per game, the highest mark by any NBA team since the league began tracking the stat in the 1996-97 season.
Adams spent his first seven seasons in the NBA with Oklahoma City before one in New Orleans.