The Bucks paved the way for Kidd by firing coach Larry Drew on Monday.
The Nets say they will receive second-round draft picks in 2015 and 2019. The 2015 pick was formerly their own.
The Nets add in a statement that they will begin a coaching search immediately.
Drew went 15-67 in his only season in Milwaukee, but there had been no indication he wouldn't be back before the Kidd situation emerged.