Green was given his first chance as a head coach on an NBA club after twice winning an NBA crown as an assistant coach with the Golden State Warriors in 2017 and 2018 before joining the Suns staff for the past two campaigns.
"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," said Pelicans team owner Gayle Benson.
"We're 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."
Phoenix star guard Devin Booker had let news of the hiring slip during the finals after the team had been told of the hiring before the decision was made public.
"He'll be the most humble, prepared coach you've ever seen in your life," Suns star guard Chris Paul said.
The Suns lost to the Milwaukee Bucks in the best-of-seven championship series four games to two.
Green played from 2003 to 2015 as an NBA guard with Philadelphia, New Orleans, Atlanta, Orlando and the Los Angeles Clippers.
"It's a blessing and an honor to get this opportunity in a special place like New Orleans," Green said. "I look forward to getting to work."