The San Antonio Spurs have 48 hours to match the offer, which includes a 15 percent trade kicker, league sources said. The Grizzlies used their full midlevel exception on the offer.
Anderson, 24, was a primary target of the Grizzlies, who've been determined to upgrade the small forward position. Anderson has had an outstanding plus-minus on defense the past two years.
The Grizzlies consider the offer sheet to Anderson an investment in the franchise's stated goal of recapturing the "Grit and Grind" culture under new coach J.B. Bickerstaff.
Anderson averaged 7.9 points and 5.4 rebounds in 26.7 minutes per game for the Spurs last season. He is expected to shoulder a larger role for the Spurs, especially if Kawhi Leonard is traded this offseason. The Spurs have been positive about retaining him.
The Spurs drafted Anderson with the 30th pick in the 2014 NBA draft, after he left UCLA following his freshman season.