Green, 30, was originally selected by the Celtics with the No. 18 pick in the 2005 draft. He played for the Celtics from 2005-07, averaging 8.9 points and 2.2 rebounds. He spent last season with the Miami Heat, averaging 8.9 points and 2.4 rebounds in 69 games (14 starts).
The 26-year-old Zeller, the 17th overall pick in the 2012 draft, appeared in 60 games for Boston last season, averaging 6.1 points and 3.0 rebounds. The 7-foot center started only three games after playing in 82 games with 59 starts the previous season when he averaged 10.2 points and 5.7 rebounds.
Zeller's deal is expected to include a non-guaranteed second season.
According to the Boston Globe, the Celtics also agreed to a guaranteed contract with their second-round draft pick, guard Demetrius Jackson, and a partially guaranteed deal with second-round forward Ben Bentil.