The position has been vacant since Roy Hodgson left by mutual consent after four years at the helm at Selhurst Park at the end of last season.
Former Arsenal captain Vieira, 45, has put pen to paper on a three-year contract with the Eagles which sees him through to 2024.
It will be the iconic Frenchman’s first senior role in the Premier League following a pair of brief stints with MLS outfit New York City and Ligue 1 club Nice.
‘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 told Palace’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.’
Vieira’s only previous coaching position in England was as manager of the Under-21 side at Manchester City which he took on after bringing an end to an illustrious playing career at the Etihad.
The 1998 World Cup winner and three-time Premier League champion will be intent on improving on Palace’s 14th-placed finish last term and a major squad overhaul is expected before the transfer window closes.
Nuno Espirito Santo had been heavily linked with the position but the Portuguese, who stepped down as Wolves boss in May, was unveiled as Tottenham’s new head coach last week.
Separate talks with ex-Borussia Dortmund head coach Lucien Favre broke down which saw Vieira jump to the top of Palace’s managerial wishlist.
On Vieira’s arrival, Palace chairman Steve Parish said: ‘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 [Freedman] in bringing in some new faces to help us all to a successful season.’
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