Vieira, 45, joins the Eagles after the decorated decade-long playing spell with Arsenal where he won the Premier League three times, while more recently has managed New York City and Nice.
The Frenchman lifted City in the MLS up to runners-up in 2017, while he was sacked at Nice in December with the side midtable after finishing fifth in 2019-20.
Palace, who finished 14th in 2020-21 and have been in the top flight since 2012, marks a return to London for the 107-time France international.
Vieira said: “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.
“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 said: “Im 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.”