Kidd retired earlier this month after one season with the New York Knicks, his 19th in the NBA. The Nets decided to hire him to replace P.J. Carlesimo despite his absence of coaching experience.
"Jason Kidd has a long and legendary history with the Nets and with the city of New York," Nets owner Mikhail Prokhorov said in a statement. "He has the fire in the belly we need, and has achieved as a player everything the Brooklyn Nets are striving to achieve. We believe he will lead us there. Welcome home, Jason."
The move reunites Kidd with the franchise he led to consecutive NBA Finals in 2002-03, when they played in New Jersey. He spent 6 1/2 seasons with the Nets, averaging 14.6 points, 9.1 assists and 7.2 rebounds, and is their career leader in numerous statistical categories.
"Jason is a proven winner and leader with an incredible wealth of basketball knowledge and experience," general manager Billy King said. "This will be a natural transition for him to move into the role of head coach, as he embodies the tough, smart and team-first mentality that we are trying to establish in Brooklyn."
Terms of the deal that made Kidd the 18th coach in franchise history were not disclosed. The Nets will introduce Kidd on Thursday during a press conference at Barclays Center.
Carlesimo wasn't retained after leading the Nets into the playoffs, where they lost to the Chicago Bulls in the first round. He went 35-19 after replacing Avery Johnson, who was fired in December.
The 40-year-old Kidd was considered one of the smartest players in the NBA, which he believes will help him make the transition into coaching.
"This is a tremendous opportunity to be named head coach of the Brooklyn Nets, and it's a role I have been studying for over the course of my playing days," Kidd said. "Championship teams are built on being prepared, playing unselfishly and being held accountable, and that's how I expect to coach this basketball team."
The Nets interviewed him this week and chose him as their coach after talking with Indiana Pacers assistant Brian Shaw earlier Wednesday.
Kidd has a close friendship with Nets point guard Deron Williams and the respect of many in the organization for his achievements as a player. He is second on the NBA's career list in assists and steals, won an NBA title with Dallas and has two Olympic gold medals.