Hodgson brought unprecedented stability to Palace, who will be playing in the top flight for a ninth consecutive seasons this year.
With 11 players out of contract this summer and investment needed in the squad, Vieira has a tough task but wants to push on from the work Hodgson has done.
“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.
“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.”
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.”