"Unfortunately, Lamar was unable to uphold the standards to return as an NBA player," Jackson said in a statement. "We found it necessary to free up the roster spot."
The Knicks also re-signed center Cole Aldrich on Friday night.
Odom's release is the latest setback in the 6-foot-10 forward's career. The Knicks signed Odom on April 16 -- the final day of the regular season -- to a two-year contract, with the second year nonguaranteed.
This gave the Knicks the opportunity to monitor Odom over the summer and decide whether he deserved a roster spot. Clearly, Jackson, who coached Odom for five seasons in Los Angeles, wasn't satisfied with Odom's approach during the trial period.
Odom's last stint in the NBA was in 2012-13 with the Los Angeles Clippers.
The Clippers and Lakers had expressed interest in signing Odom at various points of the 2013-14 season after a tumultuous summer off the floor that included his eventual divorce from reality TV star Khloe Kardashian.
During the 2013 offseason, Odom was arrested on a DUI charge and reportedly dealt with substance-abuse issues.
Aldrich was with the Knicks last season, averaging 2.0 points and 2.8 rebounds in 46 games.