The Grizzlies will receive two future second-round picks in the deal.
Wright, 27, is seen as a great perimeter defender and can guard multiple positions with his 6-foot-5 frame.
After Memphis acquired him in a deal with Toronto at the trade deadline last season, Wright averaged 12.2 points, 5.4 rebounds and 5.3 assists per game in 26 contests.
He was a key member of the young bench that elevated Toronto in 2017-18. He shot 37 percent from 3-point range in that season, a career high. If he can approach or exceed that number on more catch-and-shoot attempts playing next to Luka Doncic, he could prove to be a nice fit in Dallas.