Humphries will "most likely" be signed before the team's morning shootaround prior to Wednesday night's game in New York against the Knicks, a league source told ESPNNewYork.com.
Assuming he passes a physical, Humphries "should" be able to play on Wednesday night, the league source said.
Humphries averaged a double-double for the Nets last season, and ranked fifth in the NBA in rebounding, pulling down 10.4 boards per game.
The 26-year-old became famous over the summer after marrying celebrity Kim Kardashian, but the couple divorced after just 72 days.
Humphries had been working out in his native Minnesota recently.
Mike Mazzeo is a regular contributor to ESPNNewYork.com.