Kidd began publicly lobbying for the job last week and now finds himself with his first coaching position of any sort.
He played 6,219 games with five NBA teams, 506 of those contests over 6 1/2 seasons coming with the Nets. He helped lead the Nets to the NBA Finals in 2002 and 2003 and won the league title two years ago with the Dallas Mavericks.
"This is a tremendous opportunity to be named head coach of the Brooklyn Nets," Kidd said. "It's a role I have been studying for over the course of my playing days.
"Championship teams are built on being prepared, playing unselfishly and being held accountable, and that's how I expect to coach this basketball team. I am truly excited about this next phase of my basketball career."
Brooklyn reached the playoffs this season, but was knocked out in the opening round by the Chicago Bulls. Avery Johnson was coach of the Nets at the start of the 2012-13 season but was replaced on an interim basis last December by P.J. Carlesimo.
Kidd, 40, played 19 seasons in the NBA. He scored 17,529 points, averaging 12.6 a game. He holds the Nets career records for assists, steals and 3-point field goals.