The timing of the Pelicans' announcement was delayed due to the Suns' run to the NBA Finals, which concluded earlier this week.
"After an extensive and collaborative search, Willie stood out among an impressive group of candidates as the best person to lead our team moving forward," Pelicans owner Gayle Benson said in a statement.
"We are very happy to welcome Willie as our new head coach and we look forward to working with him to guide our team on the court as we work towards bringing a championship to New Orleans."
Pelicans executive vice president of basketball operations David Griffin called Green, who played for five different teams over his 12-year NBA career, one of the "most respected assistant coaches in the NBA."
"He brings a vast amount of basketball knowledge and experience to our team as both a coach and former player, along with exceptional leadership qualities and an innate ability to connect with players, staff and fans alike," Griffin said.
Green served as an assistant with the Golden State Warriors for three seasons (2016-19) before joining the Suns in June 2019.
The 39-year-old Green replaces former Pelicans head coach Stan Van Gundy, who mutually agreed to leave the organization after just one season. New Orleans posted a 31-41 record last season and failed to make the Western Conference Play-In Tournament.