They are the first two inductees for the year 2022, with six more ex-Premier League stars set to join them in the coming weeks.
Eight former players were inducted into the 2021 Hall of Fame.
Only players who have retired from professional football are available for selection and selection is based solely on their performance in the Premier League.
Alan Shearer, Thierry Henry, Frank Lampard, Dennis Bergkamp, Eric Cantona, Roy Keane, Steven Gerrard and David Beckham were the 2021 inductees.
Rooney is the Premier League's second all-time top scorer with 208 goals. He had two spells with Everton and won five titles with Manchester United.
"It's a huge honour for me to be named in the Premier League Hall of Fame, alongside an incredible group of players who have already been inducted," Derby County boss Rooney said.
"Growing up, I watched the Premier League as far back as I can remember.
"To enter the Hall of Fame is very special for me personally and I'm grateful to be recognised."
Crystal Palace manager Vieira was Arsenal captain when the Gunners went the entire 2003/2004 season unbeaten.
Vieira won three league titles with Arsenal and also played for Manchester City at the tail end of his career.
The 45-year-old said: "Being inducted into the Premier League Hall of Fame is a fantastic achievement. When I received the news, I thought about being a young boy playing in Senegal, or in a suburb of Paris.
"To be there with the best players in the Premier League, the best league in the world, is bigger than what I was ever thinking about. To have my name around those players makes me proud and makes me realise how good I was.
"It's not bad company to join. I was lucky to play at the same time as some of them, of course including Thierry Henry and Dennis Bergkamp. So to share the stage with them makes me realise I had a really good career.
"What really makes me happy and proud is when your name is mentioned by new, up-and-coming holding midfielders as an example of how they would like to play."
