Twenty-four-year-old Moon, who was one of Salford's stand-out players in a largely disappointing season, has signed a three-year contract with the Rhinos.
Leeds have paid an undisclosed fee for the former New Zealand Warrior, making him their second off-season signing to join fellow Australian Mitch Achurch.
"Joel is a player who we have been monitoring for a while and it is great to bring him into the club now so we can improve our squad from a position of strength," said coach Brian McDermott.
"We always said that any player we brought to the club would have to add significantly to the group and I think the fact that we have signed a player with as much experience at a young age definitely fits that criteria and he is an exciting signing not just for next season but as part of this young group moving forward."
Moon spent three seasons with the Warriors in Auckland, with his form earning him a call-up to the Indigenous All Stars squad. Previously he made 31 appearances for the Brisbane Broncos.