The 26-year-old prop or second row forward began his career in the NRL with New Zealand Warriors before making the switch to Super League ahead of the 2021 season and made 17 appearances for the Rhinos.
Vuniyayawa, who turned down the offer of a new contract from Leeds, said: “I decided to come to Salford to take on new challenges and to keep progressing in terms of my footy.
“Super League footy is quite different to NRL footy so learning to adjust to the game and how they play over here has taken a bit of time for me but I’m getting there.
“With joining the Devils, I feel like it’s a good move for me to focus on myself and what I can bring to the team.”
Salford director of rugby and operations Ian Blease said: “I am pleased and excited to bring in a quality player like King Vuniyayawa to the Red Devils for the next two seasons.
“King will add some strength and size to our pack as we continue to build our squad for 2022 and onwards.
“As a club, we will work hard with King and give him our full backing to enable him to become a leading Super League forward.”
Salford have yet to appoint a new head coach for 2022 following the surprise departure of Richard Marshall.