Zeller averaged 3.5 points and 2.4 rebounds in 51 games last season.
The Celtics waived the 7'0" center at the start of July before his $8 million deal for 2017-18 would have become guaranteed.
Zeller worked out for the Nets last week, per Michael Scotto of Basketball Insiders, and the team apparently liked what they saw.
The 2012 first-round pick spent his first two years with the Cleveland Cavaliers before being traded as part of a cap-clearing move in 2014. He then posted the best numbers of his career in 2014-15 for the Celtics, averaging 10.2 points and 5.7 rebounds per game. He appeared in every game that season while starting 59.
As Boston improved its roster, Zeller saw his role regress until averaging just 10.3 minutes per game last season.
He will now get a chance at a fresh start for a Nets team that lacks established players in the post after trading away Brook Lopez earlier in the summer. Timofey Mozgov projects to be the starting center with rookie Jarrett Allen also likely to get plenty of playing time, but Zeller should have an opportunity for minutes on this roster next season.