Green started his career in the G League (then D-League) and overseas before signing his first NBA contract with the San Antonio Spurs in 2015.

Green led Montgomery's St. Jude to the Class A State Championship in 2006 and 2008,[1] and was voted the MVP of the 2006 tournament.

He scored more than 2,500 points in his high school career, and was a member of the National Honor Society at St. Jude.

Green posted his career-high 27 points with 13 rebounds in a win over Mercer and was named the SEC Player of the Week for his efforts.

To start his junior season, Green changed his number from 32 to 1, and was named to the first team All-SEC voted on by the coaches.

[6] On November 1, he was acquired by the Austin Toros of the NBA Development League as an affiliate player of San Antonio.

Before reappearing in a game for Austin, Green returned to the NBA, signing a 10-day contract with the Memphis Grizzlies on February 2, 2015.

His minutes increased post All-Star break thanks to multiple injured teammates, and on March 6, 2016, he scored a then career-high 17 points in a loss to the Phoenix Suns.

[28] He moved to a reserve role upon returning to the line-up, and on December 7, he scored a season-high 24 points in a 107–103 win over the Pelicans.

[30] On February 7, 2019, Green and Garrett Temple were traded to the Los Angeles Clippers in exchange for Avery Bradley.

[37] On May 5, 2023, in Game 2 of the Western Conference Semifinals against the Los Angeles Lakers, Green drew a spot start with Kevon Looney suffering from illness.