Terms of the contract were not released, but Childress will get a one-year, non-guaranteed deal that could be worth the veteran's minimum, according to a source.
Childress met with Nets general manager Billy King and coach Avery Johnson on Tuesday before agreeing to the deal.
If he does make the team -- which he should -- Childress would likely fill the backup small forward role behind starter Gerald Wallace.
The Phoenix Suns used their amnesty clause option on Childress. The clause allows a team to waive one player during the new labor deal and have 100 percent of his salary taken off the cap and the luxury tax. Childress, 29, was released this offseason to give the Suns cap relief, even though they must still pay him what remains on his contract.
Childress, a six-year NBA veteran who also has played overseas, averaged 2.9 points and 2.8 rebounds in 34 games for Phoenix last season.
The Nets now have 15 players under contract, 13 of which are guaranteed. Like Childress, forward/center Andray Blatche also has a non-guaranteed deal.