ESPN's Adrian Wojnarowski first reported they were finalizing the contracts.
D'Antoni, who spent the past four seasons as head coach of the Houston Rockets, was Nash's head coach with the Phoenix Suns for four seasons from 2004-05 through 2007-08. He also coached Nash for two seasons with the Los Angeles Lakers in 2012-13 and 2013-14.
The 69-year-old D'Antoni has enjoyed head coaching stints with the Denver Nuggets, Suns, New York Knicks, Lakers and Rockets during his lengthy NBA career. He was also an assistant with the Nuggets, Suns and 76ers.
As a head coach, D'Antoni owns a solid 672-527 record, and he led teams to the playoffs on 10 occasions. While making the playoffs has rarely been an issue, he gained the reputation of being a coach who could never win the big one, as he was unable to guide a team past the conference finals.
D'Antoni is best known for his fast-paced offensive philosophy, which brought him great success with the Suns and Rockets in particular. With D'Antoni as his coach, Nash won MVP in both 2005 and 2006 while running the point in Phoenix.
D'Antoni was also at the helm in Houston when James Harden won MVP in 2018.
Udoka was a journeyman who played seven seasons for the Lakers, Knicks, Portland Trail Blazers, Spurs and Sacramento Kings. Following his retirement as a player in 2012, he spent seven seasons as an assistant in San Antonio and last season as an assistant in Philly.
The 43-year-old Udoka is one of the most highly regarded assistant coaches in the NBA and figures to get a head coaching opportunity in the near future provided the Nets perform well.
While Nash seemingly has the demeanor and knowledge needed to be a great coach, learning on the fly could be a challenge, which is why having a veteran head coach who he is familiar with in D'Antoni on the staff is a logical decision on Brooklyn's part.
Given D'Antoni's working relationship with Nash and the fact that he has often gotten the most out of his star players, he seems like a perfect fit on the Nets' coaching staff.