Dupree, a prop, was in Rhinos' full-time squad two years ago, but moved to Oldham ahead of the 2021 campaign, without having made a senior appearance.
He was named the Championship's young player of the year last season, despite playing for a relegated club and moved to Widnes Vikings in the autumn.
He has joined Salford - who Rhinos play on Sunday - in an exchange deal which sees front-rower Josh Johnson, a former Batley Bulldogs loan player, move the other way.
A Widnes statement said: "Tyler has always held the ambition of playing full-time at Super League level, which the club were aware of prior to signing him.
"After a promising start to the season, he had agreed to join Salford Red Devils for 2023.
"The opportunity arose to sign Josh for the remainder of this season, such was the decision to allow Tyler to join Salford early and with immediate effect."