Palace had been looking for a new manager following the departure of Roy Hodgson at the end of last season and looked set to appoint ex-Borussia Dortmund boss Lucien Favre until talks broke down. They eventually settled on another ex-Nice boss in Vieira, who has signed for the next three seasons.
"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," Vieira, 45, told the club's official website.
"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.
"I am also very excited to experience the atmosphere the club's supporters make at Selhurst Park and away from home too, and I know just how important that can be for the team."
Former France midfielder Vieira started his senior managerial career in 2016 when he took over at NYCFC and led them to their first playoff appearance.
He left in 2018 to take over at Nice as replacement for Favre, but was out in December 2020 following a run of five defeats in all competitions.
As a player, Vieira spent 10½ seasons in the Premier League -- nine with Arsenal, where he won the title on three occasions and the FA Cup four times -- and 18 months at Manchester City, where he retired from football.
Vieira then joined Inter Milan and won four consecutive Serie A titles before returning to England midway through the 2009-10 campaign to sign for City.