The Grizzlies announced the move on Tuesday.
The 6-1 guard averaged 21.3 points, 3.5 rebounds, 7.8 assists and 1.58 steals on .439 shooting in 37.3 minutes in 12 games for Santa Cruz this season.
Curry, 23, is the young brother of Golden State Warriors guard Stephen Curry. They are the sons of ex-NBA player Dell Curry, who made at least 40 percent from three-point range in nine of his 16 NBA seasons
Seth Curry was not drafted after this year after his senior season at Duke, during which he ranked second in the Atlantic Coast Conference in scoring at 17.5 points per game.