The Jazz also reached agreement with free-agent point guard Emmanuel Mudiay on a one-year deal, sources told ESPN.
Green leaves the Washington Wizards to join a significant group of reinforcements in Utah -- including Mike Conley Jr. and free agent Bojan Bogdanovic -- who will infuse talent into a core of Donovan Mitchell and Rudy Gobert to make the Jazz serious contenders in the Western Conference.
Green gives the Jazz a big, versatile, athletic wing player who can guard multiple positions and make shots. Green's career has been fortified with 60 playoff appearances with Oklahoma City, Boston, Memphis, the LA Clippers and Cleveland in his 12-year career.
Green, 32, averaged 12.3 points in 44 starts for the Wizards last season.
Mudiay, 23, will be playing for his third team since he was the No. 7 overall pick of the Denver Nuggets in the 2015 draft. He averaged a career-best 14.8 points to go with 3.9 assists in 42 starts last season for the New York Knicks.
Mudiay and his agent, former NBA champion B.J. Armstrong, were sold on Utah's development system under coach Quin Snyder and the chance to play behind Conley.