CBSSports.com's Ken Berger first broke the news via Twitter, adding quotes from Falk that lauded the Celtics for how they handled the unique diagnosis and surgery Green underwent.
"First class" is the way Boston handled it, Berger tweeted Falk's response.
Terms of the deal have yet to be disclosed.
With Ray Allen signing with the Miami Heat Friday night, the return of Green to Boston is that much more important. Already a fan favorite, Green's return to the court following a season sidelined with make him a great story to follow during the 2012-2013 season... but will he be effective?
Many criticized Green's game after being traded to the Celtics for Kendrick Perkins. He looked tentative and was inconsistent, averaging only 10 points and three rebounds in 26 games.
Given the current Celtics roster, Green will need to be a key cog - likely splitting time as a starter and reserve - for Doc Rivers' team to be successful.