Nash signed a four-year contract, sources told ESPN's Adrian Wojnarowski.
Jacque Vaughn, who took over coaching duties on an interim basis after Kenny Atkinson's dismissal, will remain with the club as Nash's lead assistant.
"After meeting with a number of highly accomplished coaching candidates from diverse backgrounds, we knew we had a difficult decision to make," Nets general manager Sean Marks said in a statement. "In Steve we see a leader, communicator, and mentor who will garner the respect of our players. I have had the privilege to know Steve for many years.
"One of the great on-court leaders in our game, I have witnessed firsthand his basketball acumen and selfless approach to prioritize team success. His instincts for the game, combined with an inherent ability to communicate with and unite players towards a common goal, will prepare us to compete at the highest levels of the league."
The Nets represent Nash's first foray into coaching following a 19-year career that saw him play his last official game in 2014. The 46-year-old had served as a player development consultant with the Golden State Warriors since 2015.
Nash was never publicly reported as a candidate for the Nets' head coaching role. However, Marks had quietly targeted him for some time, three sources told The New York Times' Marc Stein. Marks reportedly set his sights on the retired two-time MVP due in part to Nash's relationship with Nets star Kevin Durant following the pair's time together in Golden State.
Nash told The Undefeated's Marc J. Spears on Thursday he developed a bond with Durant while with the Warriors. The eight-time All-Star revealed he also established a strong rapport with fellow Nets star Kyrie Irving after previously crossing paths during workouts.
"Ky and I have history, not only being two point guards, but he is one of my favorite players to watch," Nash said. "He and I spent a couple days in the gym, I believe it was 2015, in New York City working out. There is a respect and admiration there for me.
"For me and Ky, our relationship is important. He is the point guard and I'm the coach, and I'm thrilled I get the opportunity to know him better and to understand him, how he plays and what he sees and be here to help him refine his gifts."
As a player, Nash opened his career with the Phoenix Suns in 1996 after being drafted 15th overall. However, the Canadian guard out of Santa Clara failed to cement a starting role in Phoenix and was shipped to the Dallas Mavericks in 1998. He had a breakout campaign in 2000-01, averaging 15.6 points per game and 7.3 assists while starring alongside Dirk Nowitzki as the Mavericks snapped a decade-long postseason drought.
After becoming a free agent in 2004, Nash returned to the Suns, where played the next eight seasons. He registered 16.3 points and 10.9 assists per game during that span - leading the league in the latter category in five of those seasons - and won back-to-back MVP awards in 2005 and 2006.
Nash was traded to the Lakers in 2012, but his brief stint in L.A. was marred by injuries. He announced his retirement in 2015 after a back issue forced him to miss the entire 2014-15 season.