Palace had been on the lookout for a new man in the dugout ever since Roy Hodgson announced his decision not to continue as manager at Selhurst Park towards the end of the 2020/2021 season.
Vieira was sacked as manager of French Ligue 1 side OGC Nice after two-and-a-half years in charge last December and was without a club.
The 45-year-old cut his managerial teeth in the Manchester City youth setup after retiring from football in 2011 before enjoying a spell in the Major League Soccer as manager of New York City FC.
"I am really excited to have this opportunity to return to the Premier League, and manage this great football club, as we begin a new chapter together," said Vieira.
"It is a project that is really appealing to me, having spoken a lot with the Chairman and Sporting Director about their ambition and plans for the whole club including the Academy. The club has fantastic foundations in place after many years in the Premier League, and I hope we can make further improvements and continue to drive the club forward.
Palace chairman Steve Parish added: "I'm delighted and excited that Patrick has agreed to join Crystal Palace as our manager following successfully learning his trade at the City Group, and experiencing positive managerial spells at New York City and then Nice, who he led to the Europa League."
"We have a lot to do to prepare in the coming weeks and I look forward to working closely with Patrick and Dougie in bringing in some new faces to help us all to a successful season."
Vieira, who won the 1998 FIFA World Cup and European Championship in 2000 with France, was captain of the ‘Invincibles’ Arsenal side who went the entire 2003/2004 Premier League season unbeaten.
