Former Arsenal captain Vieira has replaced Roy Hodgson who stepped down at the end of last season after four years at the helm.
During that time, former England boss Hodgson helped steady the ship at Selhurst Park, having taken over from Dutchman Frank De Boer who was sacked in September 2017 having only been in charge for 77 days and five matches.
The appointment of Vieira, on a contract until the summer of 2024, is something of a gamble, given his relative lack of managerial experience.
However, the 45-year-old, who was sacked by Ligue 1 side Nice in December following a poor run of form, has no doubts he can move the Eagles forwards.
“It’s a crucial period for the football club,” Vieira told Palace TV after taking his first training session with the squad in Beckenham on Monday.
“I think we’re looking forward to a new chapter, and I’m really proud and happy to be a part of it.”
Vieira added: “I think the first week is always important. To know the players, but (also) for the players to know how I want to work and the philosophy that I will want to implement in the football club.
“The first week will be when I talk to the players individually and try to understand where we are, what we want to achieve and explain to them the way I see the game and the way I want to build a team.”
Palace are set to use England’s base at St George’s Park next week as they sharpen focus towards the Premier League opener away to European champions Chelsea on August 14.
It remains to be seen just what transfer budget Vieira will be given.
The former World Cup winner, though, is confident whatever side he is able to send out at Stamford Bridge will be one ready to do things his way.
“My hope is to get the best of the players,” Vieira said.
“What I really want is to put a philosophy in place that my players understand really well, so that when they go on the field they can express themselves.
“Because there is talent and my responsibility will be to make that talent work well together. I want to see a team who is on the front foot.
“I want the team to score more goals, to have more shots on target than we used to, but at the same time to keep this kind of mental strength that the team has created in the last couple of years – to become even stronger.”
Vieira started his coaching career at another of his former clubs Manchester City, working with the academy before taking over at New York City in 2016.
With a new Palace Category One level academy facility now in place, the Eagles boss hopes to be able to utilise the pathway through to the first team.
“When you see all the young players who are coming through the academy to play for the first team, I think this football club has been working well,” Vieira said.
“So it’s working for those people – I can see if I can bring some of my experience to them to produce even more players.”
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